# LaTeX2HTML 2002-2-1 (1.71)
# Associate images original text with physical files.


$key = q/g{Z^{-d}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img713.png"
 ALT="$g{Z^{-d}}$">|; 

$key = q/{displaymath}{f_1}(x)=xhspace{0.2in}mathrm{(linear),}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img361.png"
 ALT="\begin{displaymath}
{f_1} (x) = x \hspace{0.2in} \mathrm{(linear),}
\end{displaymath}">|; 

$key = q/{displaymath}x[n]=f(a[n]cos(omegan)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img502.png"
 ALT="\begin{displaymath}
x[n] = f( a[n] \cos(\omega n))
\end{displaymath}">|; 

$key = q/{displaymath}approx{{-1}overN}cdot{{-iN}over{2pik}}cdot{{-iN}over{2pik}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="134" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1331.png"
 ALT="\begin{displaymath}
\approx {{-1} \over N} \cdot {{-iN} \over {2 \pi k}}
\cdot {{-iN} \over {2 \pi k}}
\end{displaymath}">|; 

$key = q/kA;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$kA$">|; 

$key = q/2.5omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1247.png"
 ALT="$2.5\omega$">|; 

$key = q/z[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="$z[n]$">|; 

$key = q/-0.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img612.png"
 ALT="$-0.5$">|; 

$key = q/{displaymath}x[n]=acos(omegan+phi){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="\begin{displaymath}
x[n] = a \cos (\omega n + \phi )
\end{displaymath}">|; 

$key = q/{displaymath}{calFT}left{w[n]{Z^n}right}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1127.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ w[n] {Z^n} \right \} (k)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="371" HEIGHT="218" BORDER="0"
 SRC="|."$dir".q|img373.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.10.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.23.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="312" BORDER="0"
 SRC="|."$dir".q|img818.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.23.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig09.16.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="663" HEIGHT="477" BORDER="0"
 SRC="|."$dir".q|img1227.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.16.ps}\end{figure}">|; 

$key = q/ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img239.png"
 ALT="$\ldots$">|; 

$key = q/1.5omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="$1.5\omega $">|; 

$key = q/{figure}{psfig{file=figsslashfig01.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="482" HEIGHT="391" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.09.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{div}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img396.png"
 ALT="\fbox{$\mathrm{div}$}">|; 

$key = q/{displaymath}{M_a}(phi)=W(aphi),{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img574.png"
 ALT="\begin{displaymath}
{M_a}(\phi) = W (a \phi),
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="323" HEIGHT="212" BORDER="0"
 SRC="|."$dir".q|img871.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.09.ps}\end{figure}">|; 

$key = q/a[n]+ib[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1011.png"
 ALT="$a[n] + i b[n]$">|; 

$key = q/r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img467.png"
 ALT="$r$">|; 

$key = q/R[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1206.png"
 ALT="$R[k]$">|; 

$key = q/{figure}{psfig{file=figsslashfig01.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="542" HEIGHT="608" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.11.ps}\end{figure}">|; 

$key = q/{displaymath}approx{{-i}over{2pi}}left[U^n-U^{-n}right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1322.png"
 ALT="\begin{displaymath}
\approx {{-i} \over {2 \pi}} \left [ U^n - U^{-n} \right ]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="121" BORDER="0"
 SRC="|."$dir".q|img369.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.06.ps}\end{figure}">|; 

$key = q/(3+k)pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img548.png"
 ALT="$(3+k)\pi / 2$">|; 

$key = q/1.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img793.png"
 ALT="$1.5$">|; 

$key = q/{displaymath}f(x+y)={x^2}+2xy+{y^2}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img441.png"
 ALT="\begin{displaymath}
f(x+y) = {x^2} + 2 x y + {y^2}
\end{displaymath}">|; 

$key = q/{displaymath}H(Z)={{(1-{Q_1}{Z^{-1}})cdots(1-{Q_j}{Z^{-1}})}over{(1-{P_1}{Z^{-1}})cdots(1-{P_k}{Z^{-1}})}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="263" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img889.png"
 ALT="\begin{displaymath}
H(Z) = {
{
(1 - {Q_1}{Z^{-1}}) \cdots (1 - {Q_j}{Z^{-1}})
} \over {
(1 - {P_1}{Z^{-1}}) \cdots (1 - {P_k}{Z^{-1}})
}
}
\end{displaymath}">|; 

$key = q/X[n]=X[n+Nslash2];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1262.png"
 ALT="$X[n] = X[n+N/2]$">|; 

$key = q/{displaymath}x[n]=a[1]sin(omegan)+a[2]sin(2omegan)+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="271" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1354.png"
 ALT="\begin{displaymath}
x[n] = a[1] \sin(\omega n) + a[2] \sin(2 \omega n) + \cdots
\end{displaymath}">|; 

$key = q/-{1overN};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1314.png"
 ALT="$-{1 \over N}$">|; 

$key = q/{displaymath}{2acos(alphan+phi)cos(alphan+xi)}={displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img423.png"
 ALT="\begin{displaymath}
{2 a \cos(\alpha n + \phi) \cos (\alpha n + \xi)}
=
\end{displaymath}">|; 

$key = q/{displaymath}J(Z)={{1-{Z^{-2}}}over{1+g{Z^{-2}}}}={{(1-{Z^{-1}})(1+{Z^{-1}})}over{(1-isqrt{g}{Z^{-1}})(1+isqrt{g}{Z^{-1}})}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img950.png"
 ALT="\begin{displaymath}
J(Z) =
{{
1 - {Z^{-2}}
} \over {
1 + g{Z^{-2}}
}}
=
...
... \over {
(1 - i\sqrt{g} {Z^{-1}})(1 + i\sqrt{g} {Z^{-1}})
}}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig06.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="396" BORDER="0"
 SRC="|."$dir".q|img558.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.03.ps}\end{figure}">|; 

$key = q/c=s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img762.png"
 ALT="$c=s$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="341" HEIGHT="379" BORDER="0"
 SRC="|."$dir".q|img868.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.08.ps}\end{figure}">|; 

$key = q/{displaymath}R'[k+1]=R[k+2]+R[k+1]+R[k]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1209.png"
 ALT="\begin{displaymath}
R'[k+1] = R[k+2] + R[k+1] + R[k]
\end{displaymath}">|; 

$key = q/{2^{1slash{12}}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="${2 ^ {1/{12}}}$">|; 

$key = q/x_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img247.png"
 ALT="$x_0$">|; 

$key = q/{displaymath}{{1-q}over{1-p}}=g{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img918.png"
 ALT="\begin{displaymath}
{{1-q} \over {1-p}} = g
\end{displaymath}">|; 

$key = q/{displaymath}+A[N-2]{U^{(N-2)n}}-A[N-1]{U^{(N-1)n}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1257.png"
 ALT="\begin{displaymath}
+ A[N-2]{U^{(N-2)n}} - A[N-1]{U^{(N-1)n}}
\end{displaymath}">|; 

$key = q/{displaymath}cos(acos(omega_mn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img475.png"
 ALT="\begin{displaymath}
\cos(a \cos(\omega_m n))
\end{displaymath}">|; 

$key = q/{displaymath}x[n]={-Nc_1}p[n-{M_1}]-cdots-{Nc_l}p[n-{M_l}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="305" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1297.png"
 ALT="\begin{displaymath}
x[n] = {-N c_1} p[n - {M_1}] - \cdots - {N c_l} p[n - {M_l}]
\end{displaymath}">|; 

$key = q/theta=pislash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="$\theta = \pi /4$">|; 

$key = q/{d_1},ldots,{d_j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1279.png"
 ALT="${d_1}, \ldots, {d_j}$">|; 

$key = q/c_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img238.png"
 ALT="$c_1$">|; 

$key = q/{displaymath}=e^{{-left[bsin{omegaover2}right]}^2}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="24" BORDER="0"
 SRC="|."$dir".q|img565.png"
 ALT="\begin{displaymath}
= e ^ {
{ -\left [
b \sin {\omega \over 2}
\right ] }
^2
}
\end{displaymath}">|; 

$key = q/{displaymath}overline{AB}=overline{A}cdotoverline{B}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="24" BORDER="0"
 SRC="|."$dir".q|img896.png"
 ALT="\begin{displaymath}
\overline{AB} = \overline{A} \cdot \overline{B}
\end{displaymath}">|; 

$key = q/-infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$-\infty$">|; 

$key = q/{displaymath}{x^2}[n]={1over2}+{1over2}cos(2omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img454.png"
 ALT="\begin{displaymath}
{x^2}[n] = {1 \over 2} + {1 \over 2} \cos (2\omega n)
\end{displaymath}">|; 

$key = q/{m_a}(omegan);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img573.png"
 ALT="${m_a}(\omega n)$">|; 

$key = q/k=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1092.png"
 ALT="$k=0$">|; 

$key = q/fbox{{mathrm{hip}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img280.png"
 ALT="\fbox{ $\mathrm{hip}\sim$ }">|; 

$key = q/1000slash(2f);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img840.png"
 ALT="$1000/(2f)$">|; 

$key = q/{displaymath}S[m,k];=;a;cdot;{{left|{{S[m-1,k]T'[k]}over{T[k]}}right|}^{-1}};cdot;{{{S[m-1,k]T'[k]}over{T[k]}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="383" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1192.png"
 ALT="\begin{displaymath}
S[m, k] \; = \;
a
\; \cdot \;
{
{ \left \vert
{{S[m-...
...{-1}
}
\; \cdot \;
{
{{S[m-1, k] T'[k]}
\over
{T[k]}}
}
\end{displaymath}">|; 

$key = q/(N-M,-1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$(N-M, -1)$">|; 

$key = q/2tau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$2 \tau$">|; 

$key = q/{displaymath}{A_{mathrm{RMS}}}{x[n]}=sqrt{P{x[n]}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="\begin{displaymath}
{A_{\mathrm{RMS}}} \{x[n]\} = \sqrt{P\{x[n]\}}
\end{displaymath}">|; 

$key = q/R=-{Z^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img960.png"
 ALT="$R = - {Z^2}$">|; 

$key = q/{displaymath}1=cos(0){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img452.png"
 ALT="\begin{displaymath}
1 = \cos (0)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.22.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="441" HEIGHT="491" BORDER="0"
 SRC="|."$dir".q|img979.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.22.ps}\end{figure}">|; 

$key = q/{displaymath}acos(omegan+phi){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img408.png"
 ALT="\begin{displaymath}
a \cos (\omega n + \phi)
\end{displaymath}">|; 

$key = q/M_a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img582.png"
 ALT="$M_a$">|; 

$key = q/{displaymath}{fbox{texttt{delread~}}{longrightarrowx[N-B],ldots,x[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img831.png"
 ALT="\begin{displaymath}
\fbox{\texttt{delread\&nbsp;}} \longrightarrow x[N-B], \ldots, x[N-1]
\end{displaymath}">|; 

$key = q/fbox{{mathrm{outlet}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img377.png"
 ALT="\fbox{ $\mathrm{outlet}\sim$ }">|; 

$key = q/1slash(1+b);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img572.png"
 ALT="$1/(1+b)$">|; 

$key = q/{displaymath}{calFT}left{X[n]right}(k)=left({{parbox[t][0.1in]{0in}{mbox{}}{cos(pik(N-1)slashN)-isin(pik(N-1)slashN)}right){D_N}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1089.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ X[n] \right \} (k) =
\left ( {
\parbo...
...(\pi k (N-1)/N) - i \sin(\pi k (N-1)/N)
} \right )
{D_N}(k)
\end{displaymath}">|; 

$key = q/t=3slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img193.png"
 ALT="$t=3/2$">|; 

$key = q/{figure}{psfig{file=figsslashfig02.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="488" HEIGHT="514" BORDER="0"
 SRC="|."$dir".q|img253.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.11.ps}\end{figure}">|; 

$key = q/{a^2}+{b^2}=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img971.png"
 ALT="${a^2}+{b^2}=1$">|; 

$key = q/1+1slash9+1slash25+1slash49+1slash81+cdots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1378.png"
 ALT="$1 + 1/9 + 1/25 + 1/49 + 1/81 + \cdots$">|; 

$key = q/{displaymath}approxleft[cos(Phi(k))+isin(Phi(k))right]M(k-{{alpha}over{omega}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1129.png"
 ALT="\begin{displaymath}
\approx \left [ \cos(\Phi(k)) + i \sin(\Phi(k))\right ]
M(k - {{\alpha } \over {\omega}})
\end{displaymath}">|; 

$key = q/3slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1156.png"
 ALT="$3/2$">|; 

$key = q/omega=pislashd;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img705.png"
 ALT="$\omega = \pi/d$">|; 

$key = q/{displaymath}{A_k}={1overN}left({{left[{U^{-k}}right]}^{0}}X[0]+{{left[{U^{-k}}r1}}X[1]+cdots+{{left[{U^{-k}}right]}^{N-1}}X[N-1]right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="457" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1056.png"
 ALT="\begin{displaymath}
{A_k} = {1\over N} \left (
{{\left [ {U^{-k}} \right ]} ^ ...
...dots +
{{\left [ {U^{-k}} \right ]} ^ {N-1}} X[N-1]
\right )
\end{displaymath}">|; 

$key = q/f(acdotcos(omega_mn));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img553.png"
 ALT="$f (a \cdot \cos(\omega_m n))$">|; 

$key = q/alpha=beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="$\alpha =\beta $">|; 

$key = q/{displaymath}angleleft{{{S[m-1,k+1]}over{T[k+1]}}right}=angleleft{{{S[m-1,k]}over{T[k]}}right}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1202.png"
 ALT="\begin{displaymath}
\angle \left \{ {{S[m-1, k+1]} \over {T[k+1]}} \right \} =
\angle \left \{ {{S[m-1, k]} \over {T[k]}} \right \}
\end{displaymath}">|; 

$key = q/-domega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img677.png"
 ALT="$- d \omega$">|; 

$key = q/{displaymath}pcos(n{omega_2}t+rcos({omega_1}t))+{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="176" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img596.png"
 ALT="\begin{displaymath}
p \cos ( n {\omega_2} t + r \cos ({\omega_1} t)) +
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.16.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="617" HEIGHT="741" BORDER="0"
 SRC="|."$dir".q|img285.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.16.ps}\end{figure}">|; 

$key = q/S;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img958.png"
 ALT="$S$">|; 

$key = q/omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="$\omega $">|; 

$key = q/{displaymath}left|sin({omegaover2})right|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img601.png"
 ALT="\begin{displaymath}
\left \vert \sin({\omega \over 2}) \right \vert
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="200" BORDER="0"
 SRC="|."$dir".q|img852.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.01.ps}\end{figure}">|; 

$key = q/300m+225n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img493.png"
 ALT="$300m+225n$">|; 

$key = q/{displaymath}{P{x[n]}}={1overN}left({{|x[M]|}^2}+cdots+{{|x[M+N-1]|}^2}right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="335" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="\begin{displaymath}
{P\{x[n]\}} = {1 \over N} \left (
{{\vert x[M]\vert} ^2} + \cdots + {{\vert x[M+N-1]\vert} ^2}
\right )
\end{displaymath}">|; 

$key = q/B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img311.png"
 ALT="$B$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.28.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="490" HEIGHT="241" BORDER="0"
 SRC="|."$dir".q|img837.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.28.ps}\end{figure}">|; 

$key = q/0ley[n]<N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$0 \le y[n] &lt; N$">|; 

$key = q/{figure}{psfig{file=figsslashfig10.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="479" HEIGHT="271" BORDER="0"
 SRC="|."$dir".q|img1298.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.05.ps}\end{figure}">|; 

$key = q/{displaymath}=2{b_0}+2{b_2}cosleft(2omegan+{theta_2}right)+2{b_4}cosleft(4omegan+{theta_4}right)+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img231.png"
 ALT="\begin{displaymath}
= 2 {b_0} +
2 {b_2} \cos \left ( 2 \omega n + {\theta_2} \...
... {b_4} \cos \left ( 4 \omega n + {\theta_4} \right ) + \cdots
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.19.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="550" HEIGHT="406" BORDER="0"
 SRC="|."$dir".q|img392.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.19.ps}\end{figure}">|; 

$key = q/f_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img458.png"
 ALT="$f_k$">|; 

$key = q/X'[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1271.png"
 ALT="$X'[n]$">|; 

$key = q/R(Z)=-{Z^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$R(Z) = -{Z^2}$">|; 

$key = q/X[n-d];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1107.png"
 ALT="$X[n-d]$">|; 

$key = q/A;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$A$">|; 

$key = q/{calFT}{s[n]}(0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1319.png"
 ALT="${\cal FT}\{ s[n] \}(0)$">|; 

$key = q/angle(W);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img730.png"
 ALT="$\angle(W)$">|; 

$key = q/X''[n]=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1264.png"
 ALT="$X''[n] = 0$">|; 

$key = q/x_{100};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img234.png"
 ALT="$x_{100}$">|; 

$key = q/{displaymath}R(Z)=Ucdot{{{A_n}{Z^n}+{A_{n-1}}{Z^{n-1}}+cdots+{A_0}}over{overline{A_0}{Z^n}+overline{A_1}{Z^{n-1}}+cdots+overline{A_n}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="295" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img942.png"
 ALT="\begin{displaymath}
R(Z) = U \cdot
{{
{A_n}{Z^n} + {A_{n-1}}{Z^{n-1}} + \cdot...
...}{Z^n} + \overline{A_1}{Z^{n-1}} + \cdots + \overline{A_n}
}}
\end{displaymath}">|; 

$key = q/{displaymath}20{toverd}{log_{10}}(g){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img777.png"
 ALT="\begin{displaymath}
20 {t\over d} {\log_{10}} (g)
\end{displaymath}">|; 

$key = q/{displaymath}x[M],x[M+1],ldots,x[M+N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="\begin{displaymath}
x[M], x[M+1], \ldots, x[M+N-1]
\end{displaymath}">|; 

$key = q/e^a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img522.png"
 ALT="$e^a$">|; 

$key = q/{displaymath}0.75cdotx+0.25cdoty=0.75.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img327.png"
 ALT="\begin{displaymath}
0.75 \cdot x + 0.25 \cdot y = 0.75.
\end{displaymath}">|; 

$key = q/{a_0}slash10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="${a_0}/10$">|; 

$key = q/fbox{texttt{tabsend~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1233.png"
 ALT="\fbox{\texttt{tabsend\&nbsp;}}">|; 

$key = q/-momega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1068.png"
 ALT="$-m\omega$">|; 

$key = q/(0,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1343.png"
 ALT="$(0,0)$">|; 

$key = q/{displaymath}g{Z^{-d}}H=g{Z^{-d}}+{(g{Z^{-d}})}^2+{(g{Z^{-d}})}^3+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img714.png"
 ALT="\begin{displaymath}
g{Z^{-d}} H = g{Z^{-d}} + {(g{Z^{-d}})} ^ 2 + {(g{Z^{-d}})} ^ 3 + \cdots
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="373" BORDER="0"
 SRC="|."$dir".q|img370.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.07.ps}\end{figure}">|; 

$key = q/a[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1359.png"
 ALT="$a[k]$">|; 

$key = q/{displaymath}0<d[n]<D{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img789.png"
 ALT="\begin{displaymath}
0 &lt; d[n] &lt; D
\end{displaymath}">|; 

$key = q/1slashb;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1374.png"
 ALT="$1/b$">|; 

$key = q/{d_0}+s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img808.png"
 ALT="${d_0}+s$">|; 

$key = q/fbox{texttt{hip~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1016.png"
 ALT="\fbox{ \texttt{hip\&nbsp;}}">|; 

$key = q/omega_cslashomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img593.png"
 ALT="$\omega_c/\omega$">|; 

$key = q/fbox{{mathrm{delay}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img339.png"
 ALT="\fbox{ $\mathrm{delay}$ }">|; 

$key = q/0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="$0$">|; 

$key = q/{displaymath}H(Z)=overline{Q}-{Z^{-1}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img875.png"
 ALT="\begin{displaymath}
H(Z) = \overline{Q} - {Z^{-1}}
\end{displaymath}">|; 

$key = q/{c_1}+q({c_2}-{c_1});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img620.png"
 ALT="${c_1} + q ({c_2} - {c_1})$">|; 

$key = q/{displaymath}{A_{mathrm{peak}}}{x[n]}+{A_{mathrm{peak}}}{y[n]}ge{A_{mathrm{peak}}}{x[n]+y[n]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="\begin{displaymath}
{A_{\mathrm{peak}}} \{x[n]\} +
{A_{\mathrm{peak}}} \{y[n]\} \ge
{A_{\mathrm{peak}}} \{x[n]+y[n]\}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="170" BORDER="0"
 SRC="|."$dir".q|img737.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.11.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{unpack}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img383.png"
 ALT="\fbox{ $\mathrm{unpack}$}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.20.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="346" BORDER="0"
 SRC="|."$dir".q|img805.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.20.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{moses}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img341.png"
 ALT="\fbox{ $\mathrm{moses}$ }">|; 

$key = q/{X_1}+{X_2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img673.png"
 ALT="${X_1}+{X_2}$">|; 

$key = q/{displaymath}x[n]=cos(2pinslashN),,n=0,ldots,N-1{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="255" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img264.png"
 ALT="\begin{displaymath}
x[n] = \cos(2 \pi n / N) ,  n = 0, \ldots, N-1
\end{displaymath}">|; 

$key = q/{displaymath}+{J_3}(a)cos((omega_c+3omega_m)n+{{3pi}over2})+{J_3}(a)cos((omega_c-3omega_m)n+{{3pi}over2})+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="471" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img539.png"
 ALT="\begin{displaymath}
+ {J_3}(a) \cos( (\omega_c+3\omega_m) n + {{3\pi}\over2})
...
...}(a) \cos( (\omega_c-3\omega_m) n + {{3\pi}\over2})
+ \cdots
\end{displaymath}">|; 

$key = q/sin({omegaover2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img600.png"
 ALT="$\sin({\omega \over 2})$">|; 

$key = q/NfslashR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img192.png"
 ALT="$N f / R$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="207" BORDER="0"
 SRC="|."$dir".q|img688.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.05.ps}\end{figure}">|; 

$key = q/{displaymath}{{aZ+b}over{bZ+a}}={pmsqrt{-W}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img969.png"
 ALT="\begin{displaymath}
{
{
aZ + b
} \over {
bZ + a
}
} = {
\pm \sqrt {
- W
}
}
\end{displaymath}">|; 

$key = q/{Z^n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1115.png"
 ALT="${Z^n}$">|; 

$key = q/D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="$D$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="495" HEIGHT="367" BORDER="0"
 SRC="|."$dir".q|img433.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.06.ps}\end{figure}">|; 

$key = q/N-1slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img260.png"
 ALT="$N-1/2$">|; 

$key = q/{Z^{d}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img695.png"
 ALT="${Z^{d}}$">|; 

$key = q/Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="$Q$">|; 

$key = q/{displaymath}y[n]-y[n-1]=2{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img207.png"
 ALT="\begin{displaymath}
y[n]-y[n-1] = 2
\end{displaymath}">|; 

$key = q/fbox{{mathrm{vcf}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1023.png"
 ALT="\fbox{$\mathrm{vcf}\sim$}">|; 

$key = q/{displaymath}cos((alpha-beta)n)=cos((beta-alpha)n){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img421.png"
 ALT="\begin{displaymath}
\cos((\alpha - \beta)n) = \cos((\beta - \alpha)n)
\end{displaymath}">|; 

$key = q/{displaymath}{f_3}(x)={x^4}hspace{0.2in}mathrm{(quartic).}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="161" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img363.png"
 ALT="\begin{displaymath}
{f_3} (x) = {x^4} \hspace{0.2in}\mathrm{(quartic).}
\end{displaymath}">|; 

$key = q/{displaymath}A[k]={1overN}{calFT}{X[n]}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1301.png"
 ALT="\begin{displaymath}
A[k] = {1 \over N} {\cal FT}\{X[n]\}(k)
\end{displaymath}">|; 

$key = q/{displaymath}{calFT}left{X[n]right}(k+N)={calFT}left{X[n]right}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="256" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1061.png"
 ALT="\begin{displaymath}
{\cal FT}\left \{ X[n] \right \} (k+N) =
{\cal FT}\left \{ X[n] \right \} (k)
\end{displaymath}">|; 

$key = q/fbox{{mathrm{send}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img289.png"
 ALT="\fbox{ $\mathrm{send}\sim$ }">|; 

$key = q/{displaymath}{calFT}left{X[n]right}(k)=left{array{{ll}N&{k=0}0&{k=1,ldots,N-1}array{right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1079.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ X[n] \right \} (k) =
\left \{
\begin{...
...}
N &amp; {k=0} \\\\
0 &amp; {k=1, \ldots, N-1}
\end{array} \right .
\end{displaymath}">|; 

$key = q/{displaymath}cos((pi+omega)n+phi)=cos((pi+omega)n+phi-2pin){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="314" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img302.png"
 ALT="\begin{displaymath}
\cos((\pi + \omega)n + \phi) = \cos((\pi + \omega)n + \phi - 2\pi n)
\end{displaymath}">|; 

$key = q/12omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1371.png"
 ALT="$12\omega$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="542" HEIGHT="245" BORDER="0"
 SRC="|."$dir".q|img913.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.13.ps}\end{figure}">|; 

$key = q/xi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1084.png"
 ALT="$\xi$">|; 

$key = q/x_{50};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img233.png"
 ALT="$x_{50}$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="399" BORDER="0"
 SRC="|."$dir".q|img402.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.01.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{samphold}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img284.png"
 ALT="\fbox{ $\mathrm{samphold}\sim$ }">|; 

$key = q/{figure}{psfig{file=figsslashfig01.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="225" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.07.ps}\end{figure}">|; 

$key = q/|P|=0.9;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$\vert P\vert=0.9$">|; 

$key = q/{displaymath}Y[n]=X[n-d]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img671.png"
 ALT="\begin{displaymath}
Y[n] = X[n-d]
\end{displaymath}">|; 

$key = q/f(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img460.png"
 ALT="$f(x)$">|; 

$key = q/|H(omega)|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img725.png"
 ALT="$\vert H(\omega)\vert$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="359" HEIGHT="371" BORDER="0"
 SRC="|."$dir".q|img487.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.10.ps}\end{figure}">|; 

$key = q/gW^{-d};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img731.png"
 ALT="$gW^{-d}$">|; 

$key = q/fbox{{mathrm{dbtorms}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="\fbox{ $ \mathrm{dbtorms} $}">|; 

$key = q/0,...,N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="$0, ..., N-1$">|; 

$key = q/y[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="$y[n]$">|; 

$key = q/{displaymath}x[n]=cos(omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img453.png"
 ALT="\begin{displaymath}
x[n] = \cos (\omega n)
\end{displaymath}">|; 

$key = q/{displaymath}f(x[n+tau])=f(x[n]){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img443.png"
 ALT="\begin{displaymath}
f(x[n+\tau]) = f(x[n])
\end{displaymath}">|; 

$key = q/a=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img469.png"
 ALT="$a=0$">|; 

$key = q/{displaymath}={b_0}+{b_1}cosleft(omegan+{theta_1}right)+{b_2}cosleft(2omegan+{theta_2}right)+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img229.png"
 ALT="\begin{displaymath}
=
{b_0} +
{b_1} \cos \left ( \omega n + {\theta_1} \right...
...
{b_2} \cos \left ( 2 \omega n + {\theta_2} \right ) + \cdots
\end{displaymath}">|; 

$key = q/f_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img507.png"
 ALT="$f_0$">|; 

$key = q/{displaymath}{x_{100}}[n]={a_0}+{a_1}cosleft(omegan+{phi_1}right)+{a_2}cosleft(2omegan+{phi_2}right)+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img222.png"
 ALT="\begin{displaymath}
{x_{100}}[n] = {a_0} +
{a_1} \cos \left ( \omega n + {\phi...
...+
{a_2} \cos \left ( 2 \omega n + {\phi_2} \right ) + \cdots
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig10.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="389" BORDER="0"
 SRC="|."$dir".q|img1373.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.11.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig09.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="423" BORDER="0"
 SRC="|."$dir".q|img1157.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.08.ps}\end{figure}">|; 

$key = q/beta=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="$\beta =0$">|; 

$key = q/{displaymath}x[n]={{N^2}over{2{pi^2}(MN-2{M^2})}}left[{parbox[t][0.12in]{0in}{mbox{}}{{cos(omega(n-M))}-{cos(omega(n+M))}right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1350.png"
 ALT="\begin{displaymath}
x[n] = {{N^2} \over {2{\pi ^ 2} (MN - 2{M^2})}} \left [
\p...
...{}}
{\cos ( \omega (n-M))} - {\cos ( \omega (n+M))}
\right .
\end{displaymath}">|; 

$key = q/{displaymath}left.-{sin(omegan)}+{{sin(2omegan)}over2}-{{sin(3omegan)}over3}pmcdotsright]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1338.png"
 ALT="\begin{displaymath}
\left .
-{\sin ( \omega n )}
+ {{\sin ( 2 \omega n)} \over 2}
- {{\sin ( 3 \omega n)} \over 3}
\pm \cdots
\right ]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig09.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="384" BORDER="0"
 SRC="|."$dir".q|img1121.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.03.ps}\end{figure}">|; 

$key = q/{displaymath}x[n]=cos(omega_cn)*cos(acos(omega_mn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img471.png"
 ALT="\begin{displaymath}
x[n] = \cos(\omega_c n) * \cos(a \cos(\omega_m n))
\end{displaymath}">|; 

$key = q/fbox{{mathrm{mod}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img395.png"
 ALT="\fbox{ $\mathrm{mod}$}">|; 

$key = q/{displaymath}angleS[m,k]=angleS[m-1,k]+left(angleT'[k]-angleT[k]right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="299" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1190.png"
 ALT="\begin{displaymath}
\angle S[m, k] = \angle S[m-1, k] +
\left ( \angle T'[k] - \angle T[k] \right )
\end{displaymath}">|; 

$key = q/omegad;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img703.png"
 ALT="$\omega d $">|; 

$key = q/MslashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1356.png"
 ALT="$M/N$">|; 

$key = q/{displaymath}X[n]=A[0]+A[1]{U^n}+cdots+A[N-1]{U^{(N-1)n}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="331" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1252.png"
 ALT="\begin{displaymath}
X[n] = A[0] + A[1]{U^n} + \cdots + A[N-1]{U^{(N-1)n}}
\end{displaymath}">|; 

$key = q/Z=a+bi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img637.png"
 ALT="$Z=a+bi$">|; 

$key = q/{displaymath}{x_{100}}[2n]={x_{50}}[n]+{x_{50}}[n+{pioveromega}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="209" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img225.png"
 ALT="\begin{displaymath}
{x_{100}}[2n] = {x_{50}}[n] + {x_{50}}[n+{\pi \over \omega}]
\end{displaymath}">|; 

$key = q/H;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="$H$">|; 

$key = q/{displaymath}A+overline{A}=2,mathrm{re}(A){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img897.png"
 ALT="\begin{displaymath}
A + \overline{A} = 2   \mathrm{re} (A)
\end{displaymath}">|; 

$key = q/{displaymath}{m_a}[n]=f(acos(omegan)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="147" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img561.png"
 ALT="\begin{displaymath}
{m_a}[n] = f (a \cos(\omega n))
\end{displaymath}">|; 

$key = q/fbox{{mathrm{rfft}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1219.png"
 ALT="\fbox{$\mathrm{rfft}\sim$}">|; 

$key = q/{displaymath}f(x+y)[n+tau]=f(x+y)[n].{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img448.png"
 ALT="\begin{displaymath}
f(x+y)[n + \tau] = f(x+y)[n].
\end{displaymath}">|; 

$key = q/{displaymath}{m_a}[n]=g(bsin{omegaover2}n){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img567.png"
 ALT="\begin{displaymath}
{m_a}[n] = g ( b \sin {\omega \over 2} n )
\end{displaymath}">|; 

$key = q/(-1)^k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1213.png"
 ALT="$(-1)^k$">|; 

$key = q/fbox{{mathrm{line}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="\fbox{ $ \mathrm{line}\sim $}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="320" HEIGHT="398" BORDER="0"
 SRC="|."$dir".q|img217.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.05.ps}\end{figure}">|; 

$key = q/d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="$d$">|; 

$key = q/x[1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img683.png"
 ALT="$x[1]$">|; 

$key = q/{figure}{psfig{file=figsslashfig01.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="438" HEIGHT="373" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.08.ps}\end{figure}">|; 

$key = q/{displaymath}W(phi)={1over2}left(cos(phi)+1right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img577.png"
 ALT="\begin{displaymath}
W(\phi) = {1\over2} \left ( \cos(\phi) + 1 \right )
\end{displaymath}">|; 

$key = q/k>1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1096.png"
 ALT="$k&gt;1$">|; 

$key = q/n=10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="$n=10$">|; 

$key = q/{displaymath}=left[cos(Phi(k))+isin(Phi(k))right]{D_N}(k-{{alpha}over{omega}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="265" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1117.png"
 ALT="\begin{displaymath}
= \left [ \cos(\Phi(k)) + i \sin(\Phi(k))\right ]
{D_N}(k - {{\alpha } \over {\omega}})
\end{displaymath}">|; 

$key = q/{displaymath}={acosleft(2alphan+(phi+xi)right)}+{acosleft(phi-xiright)}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="266" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img424.png"
 ALT="\begin{displaymath}
=
{a \cos \left ( 2 \alpha n + (\phi + \xi) \right ) }
+
{a \cos \left ( \phi - \xi \right ) }
.
\end{displaymath}">|; 

$key = q/{displaymath}{x^5}[n]={1over16}cos(-3omegan)+{4over16}cos(-omegan)+{6over16}cos(omegan)+{4over16}cos(3omegan)+{1over16}cos(5omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img457.png"
 ALT="\begin{displaymath}
{x^5}[n] = {1 \over 16} \cos (-3\omega n) + {4 \over 16} \c...
... \over 16} \cos (3 \omega n)
+ {1 \over 16} \cos (5 \omega n)
\end{displaymath}">|; 

$key = q/0lenleN-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1286.png"
 ALT="$0 \le n \le N-1$">|; 

$key = q/fbox{{mathrm{q8_rsqrt}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1244.png"
 ALT="\fbox{$\mathrm{q8\_rsqrt}\sim$}">|; 

$key = q/f=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$f=0$">|; 

$key = q/{displaymath}x[n]=cos(2pinslashN),,n=0,ldots,N{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img266.png"
 ALT="\begin{displaymath}
x[n] = \cos(2 \pi n / N) ,  n = 0, \ldots, N
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.24.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="510" HEIGHT="291" BORDER="0"
 SRC="|."$dir".q|img823.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.24.ps}\end{figure}">|; 

$key = q/k^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$k^2$">|; 

$key = q/{displaymath}{calFT}left{(cos(alpha)+isin(alpha))X[n]right}(k)={calFT}left{X[n]right}(k-{{alphaN}over{2pi}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1114.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ (\cos(\alpha) + i \sin(\alpha)) X[n] \ri...
...l FT} \left \{ X[n] \right \} (k - {{\alpha N} \over {2 \pi}})
\end{displaymath}">|; 

$key = q/t_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$t_1$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.20.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="459" HEIGHT="598" BORDER="0"
 SRC="|."$dir".q|img393.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.20.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="453" BORDER="0"
 SRC="|."$dir".q|img773.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.15.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="609" HEIGHT="304" BORDER="0"
 SRC="|."$dir".q|img221.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.09.ps}\end{figure}">|; 

$key = q/{displaymath}{P_2}=overline{P_1}=(1-beta)(cosomega-isinomega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img922.png"
 ALT="\begin{displaymath}
{P_2} = \overline{P_1} = (1 - \beta) (\cos \omega - i \sin \omega)
\end{displaymath}">|; 

$key = q/{displaymath}{a_1}cos({alpha_1}n)+cdots+{a_k}cos({alpha_k}n){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img428.png"
 ALT="\begin{displaymath}
{a_1} \cos({\alpha _1} n ) + \cdots + {a_k} \cos({\alpha _k} n )
\end{displaymath}">|; 

$key = q/(k+q)omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img605.png"
 ALT="$(k+q)\omega$">|; 

$key = q/{displaymath}P{x[n]+y[n]}=P{x[n]}+P{y[n]}+2cdot{mathrm{COV}}{x[n],y[n]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="405" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="\begin{displaymath}
P \{x[n] + y[n]\} = P \{x[n]\} + P \{y[n]\}
+ 2 \cdot {\mathrm{COV}} \{ x[n] , y[n] \}
\end{displaymath}">|; 

$key = q/{displaymath}y[n]-y[n-1]=1{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img205.png"
 ALT="\begin{displaymath}
y[n]-y[n-1] = 1
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="554" HEIGHT="194" BORDER="0"
 SRC="|."$dir".q|img272.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.12.ps}\end{figure}">|; 

$key = q/P=0.9;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="$P=0.9$">|; 

$key = q/p=1-dslashsqrt{g};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img916.png"
 ALT="$p = 1 - d / \sqrt{g}$">|; 

$key = q/{displaymath}s[n]=nslashN-1slash2{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1285.png"
 ALT="\begin{displaymath}
s[n] = n/N - 1/2
\end{displaymath}">|; 

$key = q/fbox{{mathrm{delread}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img822.png"
 ALT="\fbox{$\mathrm{delread}\sim$}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="204" BORDER="0"
 SRC="|."$dir".q|img651.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.02.ps}\end{figure}">|; 

$key = q/(1+r)omega_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img466.png"
 ALT="$(1+r) \omega_c$">|; 

$key = q/fbox{{mathrm{dbtorms}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="\fbox{ $ \mathrm{dbtorms}\sim $}">|; 

$key = q/w[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1123.png"
 ALT="$w[n]$">|; 

$key = q/i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img646.png"
 ALT="$i$">|; 

$key = q/{displaymath}={1overN}left[X[0]+{U^{-k}}X[1]+cdots+{U^{-(N-1)k}}X[N-1]right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="351" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1302.png"
 ALT="\begin{displaymath}
= {1 \over N} \left [ X[0] +
{U^{-k}} X[1] + \cdots +
{U^{-(N-1)k}} X[N-1] \right ]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="174" BORDER="0"
 SRC="|."$dir".q|img356.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.01.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig01.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="447" HEIGHT="301" BORDER="0"
 SRC="|."$dir".q|img160.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.14.ps}\end{figure}">|; 

$key = q/beta=pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="$\beta =\pi $">|; 

$key = q/nomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img654.png"
 ALT="$n\omega$">|; 

$key = q/fbox{{mathrm{ftom}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="\fbox{ $ \mathrm{ftom} $}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.25.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="223" HEIGHT="318" BORDER="0"
 SRC="|."$dir".q|img987.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.25.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{fiddle}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img489.png"
 ALT="\fbox{$\mathrm{fiddle}\sim$}">|; 

$key = q/{displaymath}S[m,k]={calFT}{w(n)X[n-mH]}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1151.png"
 ALT="\begin{displaymath}
S[m, k] = {\cal FT}\{w(n)X[n-mH]\} (k)
\end{displaymath}">|; 

$key = q/p[n-(N-M)];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="112" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1348.png"
 ALT="$p[n-(N-M)]$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="207" BORDER="0"
 SRC="|."$dir".q|img1133.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.05.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="168" BORDER="0"
 SRC="|."$dir".q|img879.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.10.ps}\end{figure}">|; 

$key = q/a=cos(theta)=sin(theta)=sqrt{1slash2}approx0.7071;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img763.png"
 ALT="$a = \cos(\theta) = \sin(\theta) = \sqrt{1/2} \approx 0.7071$">|; 

$key = q/-a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img426.png"
 ALT="$-a$">|; 

$key = q/R=44100;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img297.png"
 ALT="$R=44100$">|; 

$key = q/c(phi);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img594.png"
 ALT="$c(\phi)$">|; 

$key = q/2N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1200.png"
 ALT="$2N$">|; 

$key = q/{displaymath}Phi(k)=-picdot(k-{{alpha}over{omega}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1130.png"
 ALT="\begin{displaymath}
\Phi(k) = - \pi \cdot (k - {{\alpha } \over {\omega}})
\end{displaymath}">|; 

$key = q/J;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img945.png"
 ALT="$J$">|; 

$key = q/{U^{Nslash2}}=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1255.png"
 ALT="${U^{N/2}} = -1$">|; 

$key = q/{w_1},ldots{w_j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img768.png"
 ALT="${w_1}, \ldots {w_j}$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="540" HEIGHT="380" BORDER="0"
 SRC="|."$dir".q|img914.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.14.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="257" BORDER="0"
 SRC="|."$dir".q|img681.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.04.ps}\end{figure}">|; 

$key = q/NslashR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1250.png"
 ALT="$N/R$">|; 

$key = q/fbox{{mathrm{bp}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1018.png"
 ALT="\fbox{$\mathrm{bp}\sim$}">|; 

$key = q/{displaymath}{X_n}=2,mathrm{re}(A{Z^n})=A{Z^n}+overline{A}{{overline{Z}}^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img893.png"
 ALT="\begin{displaymath}
{X_n} = 2   \mathrm{re}(A{Z^n}) = A{Z^n} + \overline{A}
{{\overline{Z}}^n}
\end{displaymath}">|; 

$key = q/{displaymath}{calFT}{p[n]}(k)approx{{-1}overN}cdot{{-iN}over{2pik}}cdot{calFT}{s[n]}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1330.png"
 ALT="\begin{displaymath}
{\cal FT}\{ p[n] \} (k) \approx
{{-1} \over N} \cdot {{-iN} \over {2 \pi k}} \cdot {\cal FT}\{ s[n] \} (k)
\end{displaymath}">|; 

$key = q/H=Y[n]slashX[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img720.png"
 ALT="$H=Y[n]/X[n]$">|; 

$key = q/k+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img602.png"
 ALT="$k+1$">|; 

$key = q/fbox{{mathrm{noise}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1020.png"
 ALT="\fbox{$\mathrm{noise}\sim$}">|; 

$key = q/{displaymath}={{{{({noverN}-{Nover{2N}})}^2}-{{({{n}overN}-{{N-2}over{2N}})}^2}}over{2}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1327.png"
 ALT="\begin{displaymath}
= {
{
{{({n\over N} - {N\over {2N}})}^2} -
{{({{n}\over N} - {{N - 2}\over {2N}})}^2}
} \over {
2
}}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig06.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="109" BORDER="0"
 SRC="|."$dir".q|img585.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.07.ps}\end{figure}">|; 

$key = q/f(t)=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img299.png"
 ALT="$f(t)=1$">|; 

$key = q/{displaymath}x[n]=cos(2pi(n-1)slashN),,n=0,ldots,N+2{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img271.png"
 ALT="\begin{displaymath}
x[n] = \cos(2 \pi (n-1) / N) ,  n = 0, \ldots, N+2
\end{displaymath}">|; 

$key = q/fbox{texttt{fft~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1216.png"
 ALT="\fbox{\texttt{fft\&nbsp;}}">|; 

$key = q/overline{Z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img956.png"
 ALT="$\overline{Z}$">|; 

$key = q/n=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="$n=0$">|; 

$key = q/1slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$1/2$">|; 

$key = q/{displaymath}t[n]=y[n]-y[n-1]=1-(d[n]-d[n-1]){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="306" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img791.png"
 ALT="\begin{displaymath}
t[n] = y[n] - y[n-1] = 1 - (d[n] - d[n-1])
\end{displaymath}">|; 

$key = q/{displaymath}H=1+g{Z^{-d}}+{(g{Z^{-d}})}^2+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img712.png"
 ALT="\begin{displaymath}
H = 1 + g{Z^{-d}} + {(g{Z^{-d}})} ^ 2 + \cdots
\end{displaymath}">|; 

$key = q/0:1:2cdots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img405.png"
 ALT="$0:1:2\cdots$">|; 

$key = q/{displaymath}left{array{{ll}{sqrt{{s[k]-m[k]}over{s[k]}}}&{s[k]>m[k]}0&mbox{otherwise}array{right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img1230.png"
 ALT="\begin{displaymath}
\left \{
\begin{array}{ll}
{\sqrt{{s[k]-m[k]}\over {s[k]}...
... {s[k] &gt; m[k]} \\\\
0 &amp; \mbox{otherwise}
\end{array} \right .
\end{displaymath}">|; 

$key = q/1slashoverline{P};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img984.png"
 ALT="$1/\overline{P}$">|; 

$key = q/{figure}{psfig{file=figsslashfig01.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="439" HEIGHT="336" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.01.ps}\end{figure}">|; 

$key = q/{displaymath}P({x_1}[n],ldots,{x_r}[n])=P({x_1}[n])+cdots+P({x_r}[n]){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img739.png"
 ALT="\begin{displaymath}
P({x_1}[n] , \ldots , {x_r}[n]) = P({x_1}[n]) + \cdots + P({x_r}[n])
\end{displaymath}">|; 

$key = q/fbox{texttt{rzero_rev~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1029.png"
 ALT="\fbox{ \texttt{rzero\_rev\&nbsp;}}">|; 

$key = q/{displaymath}H={1over{1-g{Z^{-d}}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img716.png"
 ALT="\begin{displaymath}
H = {1 \over {1 - g{Z^{-d}}}}
\end{displaymath}">|; 

$key = q/X={x_1}+{x_2}i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img755.png"
 ALT="$X={x_1} + {x_2}i$">|; 

$key = q/lfloorxrfloor;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img248.png"
 ALT="$\lfloor x \rfloor$">|; 

$key = q/{displaymath}={1over2}{left[{{parbox[t][0.1in]{0in}{mbox{}}{{cosleft((alpha+beta)right)}+{cosleft((alpha-beta)n+(phi-xi)right)}}right]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="391" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img414.png"
 ALT="\begin{displaymath}
= {1 \over 2} { \left [ {
\parbox[t][0.1in]{0in}{\mbox{}}...
...t ( (\alpha - \beta) n + (\phi - \xi) \right ) }
} \right ] }
\end{displaymath}">|; 

$key = q/Q{Z^{-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img866.png"
 ALT="$Q{Z^{-1}}$">|; 

$key = q/harmonic;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img406.png"
 ALT="$harmonic$">|; 

$key = q/fbox{texttt{delread~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img821.png"
 ALT="\fbox{ \texttt{delread\&nbsp;}}">|; 

$key = q/{displaymath}{y_{mathrm{INT}}}(x)={a_0}+{a_1}(x-{x_0})+{a_2}{{({x-x_0})}^2}+cdots+{a_n}{{({x-x_0})}^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img245.png"
 ALT="\begin{displaymath}
{y_{\mathrm{INT}}}(x) =
{a_0} + {a_1} (x - {x_0}) + {a_2} {{({x - x_0})}^ 2 } + \cdots +
{a_n} {{({x - x_0})}^ n }
\end{displaymath}">|; 

$key = q/{displaymath}f(x)={f_0}+{f_2}{x^2}+{f_4}{x^4}+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img459.png"
 ALT="\begin{displaymath}
f(x) = {f_0} + {f_2}{x^2} + {f_4}{x^4} + \cdots
\end{displaymath}">|; 

$key = q/tslashd;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img775.png"
 ALT="$t/d$">|; 

$key = q/1-p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img910.png"
 ALT="$1-p$">|; 

$key = q/{displaymath}...,x[n-1],x[n],x[n+1],...{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="189" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="\begin{displaymath}
..., x[n-1], x[n], x[n+1], ...
\end{displaymath}">|; 

$key = q/fbox{{mathrm{mtof}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="\fbox{ $ \mathrm{mtof} $}">|; 

$key = q/fbox{{mathrm{tabosc4}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img273.png"
 ALT="\fbox{ $ \mathrm{tabosc4}\sim $}">|; 

$key = q/P<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img982.png"
 ALT="$P&lt;1$">|; 

$key = q/{displaymath}S[m,k];=;{{left|R[k]right|}^{-1}}cdot{{R[k]T'[k]}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1204.png"
 ALT="\begin{displaymath}
S[m, k] \; = \;
{
{ \left \vert
R[k]
\right \vert}
^
{-1}
}
\cdot
{
{R[k] T'[k]}
}
\end{displaymath}">|; 

$key = q/{displaymath}{D_N}(k)approx{{Nsin(pik)}over{pik}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="138" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1136.png"
 ALT="\begin{displaymath}
{D_N}(k) \approx {
{N \sin(\pi k) } \over {\pi k}
}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig03.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="196" BORDER="0"
 SRC="|."$dir".q|img328.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.05.ps}\end{figure}">|; 

$key = q/{displaymath}{x^3}[n]={1over4}cos(-omegan)+{2over4}cos(omegan)+{1over4}cos(3omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="317" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img455.png"
 ALT="\begin{displaymath}
{x^3}[n] = {1 \over 4} \cos (-\omega n) + {2 \over 4} \cos (\omega n)
+ {1 \over 4} \cos (3 \omega n)
\end{displaymath}">|; 

$key = q/Nslash2Mapprox1slash17;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1364.png"
 ALT="$N/2M \approx 1/17$">|; 

$key = q/{displaymath}{cos(omega(n-M))}-{cos(omega(n+M))}=2sin(2piMslashN)sin(omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1353.png"
 ALT="\begin{displaymath}
{\cos ( \omega (n-M))} - {\cos ( \omega (n+M))} =
2 \sin (2 \pi M / N) \sin ( \omega n)
\end{displaymath}">|; 

$key = q/(1-r)omega_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img465.png"
 ALT="$(1-r)\omega_c $">|; 

$key = q/q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img592.png"
 ALT="$q$">|; 

$key = q/{displaymath}{H_{mathrm{im}}}(Z)={{mathrm{im}(P){Z^{-1}}}over{(1-{P}{Z^{-1}})(1-{overline{P}}{Z^{-1}})}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img906.png"
 ALT="\begin{displaymath}
{H_{\mathrm{im}}}(Z) = {{
\mathrm{im} (P) {Z^{-1}}
} \over {
(1 - {P}{Z^{-1}}) (1 - {\overline{P}}{Z^{-1}})
}}
\end{displaymath}">|; 

$key = q/sqrt2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$\sqrt 2$">|; 

$key = q/1+aomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img804.png"
 ALT="$1 + a \omega$">|; 

$key = q/{displaymath}H-g{Z^{-d}}H=1{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img715.png"
 ALT="\begin{displaymath}
H - g{Z^{-d}} H = 1
\end{displaymath}">|; 

$key = q/alpha=1.5omega=3pislashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$\alpha =1.5\omega =3\pi /N$">|; 

$key = q/fbox{{mathrm{poly}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img397.png"
 ALT="\fbox{ $\mathrm{poly}$}">|; 

$key = q/S[m-1,k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1198.png"
 ALT="$S[m-1,k]$">|; 

$key = q/fbox{texttt{makenote}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img398.png"
 ALT="\fbox{ \texttt{makenote}}">|; 

$key = q/T[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1199.png"
 ALT="$T[k]$">|; 

$key = q/{displaymath}m=69+12cdot{log_2}(fslash440){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="\begin{displaymath}
m = 69 + 12 \cdot {\log _ 2} (f/440)
\end{displaymath}">|; 

$key = q/a_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$a_0$">|; 

$key = q/k<-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1097.png"
 ALT="$k &lt; -1$">|; 

$key = q/2pislashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$2\pi/N$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="628" HEIGHT="388" BORDER="0"
 SRC="|."$dir".q|img365.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.03.ps}\end{figure}">|; 

$key = q/inharmonic;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img407.png"
 ALT="$inharmonic$">|; 

$key = q/2f,4f,6fcdots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img842.png"
 ALT="$2f, 4f, 6f\cdots$">|; 

$key = q/R(S(Z))=W;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img967.png"
 ALT="$R(S(Z)) = W$">|; 

$key = q/fp+d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img390.png"
 ALT="$fp+d$">|; 

$key = q/{displaymath}R'[k]=R[k+1]+R[k]+R[k-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1208.png"
 ALT="\begin{displaymath}
R'[k] = R[k+1] + R[k] + R[k-1]
\end{displaymath}">|; 

$key = q/Y[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img717.png"
 ALT="$Y[n]$">|; 

$key = q/cdots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img430.png"
 ALT="$\cdots$">|; 

$key = q/omega_b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img586.png"
 ALT="$\omega_b$">|; 

$key = q/{figure}{psfig{file=figsslashfig03.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="535" HEIGHT="416" BORDER="0"
 SRC="|."$dir".q|img334.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.09.ps}\end{figure}">|; 

$key = q/{displaymath}angle({H_1}(Z))-angle({H_2}(Z))approxleft{array{{ll}pislash2&{0<angle(Z)<pi}-pislash2&{-pi<angle(Z)<0}array{right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1008.png"
 ALT="\begin{displaymath}
\angle({H_1}(Z)) - \angle({H_2}(Z)) \approx
\left \{
\be...
...pi} \\\\
-\pi/2 &amp; {-\pi &lt; \angle(Z) &lt; 0}
\end{array} \right .
\end{displaymath}">|; 

$key = q/{displaymath}b=rsin(theta){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img636.png"
 ALT="\begin{displaymath}
b = r \sin (\theta)
\end{displaymath}">|; 

$key = q/e;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img977.png"
 ALT="$e$">|; 

$key = q/{displaymath}c(phi)=c(omegan)=pcos(komegan)+qcos((k+1)omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img589.png"
 ALT="\begin{displaymath}
c(\phi) = c(\omega n) = p \cos( k \omega n) + q \cos( (k+1) \omega n)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig03.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="224" BORDER="0"
 SRC="|."$dir".q|img337.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.12.ps}\end{figure}">|; 

$key = q/{d_1}+cdots+{d_j}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1291.png"
 ALT="${d_1} + \cdots + {d_j} = 0$">|; 

$key = q/{displaymath}{Z_1}{Z_2}={r_1}{r_2}cdot{left[{cos({theta_1})cos({theta_2})-sin({theta_1})sin({theta_2})}right.},+{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img643.png"
 ALT="\begin{displaymath}
{Z_1}{Z_2} = {r_1}{r_2} \cdot
{ \left [ {
\cos({\theta_1...
...a_2}) -
\sin({\theta_1}) \sin({\theta_2})
} \right . }   +
\end{displaymath}">|; 

$key = q/{displaymath}approx(1-iomegak){calFT}{x[n]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1306.png"
 ALT="\begin{displaymath}
\approx (1 - i \omega k) {\cal FT}\{ x[n] \}
\end{displaymath}">|; 

$key = q/{x_1}[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img740.png"
 ALT="${x_1}[n]$">|; 

$key = q/{displaymath}y[n]+x[n](z[n]-y[n]){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img189.png"
 ALT="\begin{displaymath}
y[n] + x[n](z[n]-y[n])
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="148" BORDER="0"
 SRC="|."$dir".q|img724.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.10.ps}\end{figure}">|; 

$key = q/(M,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="$(M, 1)$">|; 

$key = q/alpha-beta<0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img420.png"
 ALT="$\alpha-\beta&lt;0$">|; 

$key = q/{displaymath}={V^{d}}X[0]+{V^{d+1}}X[1]+cdots+{V^{d+N-1}}X[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="333" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1103.png"
 ALT="\begin{displaymath}
=
{V ^ {d}} X[0] +
{V ^ {d+1}} X[1] +
\cdots +
{V ^ {d+N-1}} X[N-1]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="305" BORDER="0"
 SRC="|."$dir".q|img371.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.08.ps}\end{figure}">|; 

$key = q/{displaymath}sin(acos(omegan))=2{J_1}(a)cos(omegan)-2{J_3}(a)cos(3omegan)+2{J_5}(a)cos(5omegan)mpcdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="512" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img529.png"
 ALT="\begin{displaymath}
\sin(a \cos(\omega n)) =
2 {J_1}(a) \cos(\omega n)
- 2{J_3}(a) \cos(3 \omega n)
+ 2{J_5}(a) \cos(5 \omega n) \mp \cdots
\end{displaymath}">|; 

$key = q/{displaymath}=2cos(omegadslash2){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img700.png"
 ALT="\begin{displaymath}
= 2 \cos(\omega d / 2)
\end{displaymath}">|; 

$key = q/X[-n]=X[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1275.png"
 ALT="$X[-n] = X[n]$">|; 

$key = q/{displaymath}0,2omega_m,4omega_m,ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img477.png"
 ALT="\begin{displaymath}
0, 2\omega_m, 4\omega_m, \ldots
\end{displaymath}">|; 

$key = q/x[N],ldots,x[N+B-1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img830.png"
 ALT="$x[N], \ldots, x[N+B-1]$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.30.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="591" HEIGHT="386" BORDER="0"
 SRC="|."$dir".q|img845.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.30.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig01.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="206" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.10.ps}\end{figure}">|; 

$key = q/Zoverline{Z};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img878.png"
 ALT="$Z\overline{Z}$">|; 

$key = q/beta>alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\beta &gt; \alpha $">|; 

$key = q/{displaymath}{y_{mathrm{INT}}}(x)=y[{x_0}]+(y[{x_0}+1]-y[{x_0}])cdot(x-{x_0}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img249.png"
 ALT="\begin{displaymath}
{y_{\mathrm{INT}}}(x) =
y[{x_0}] + (y[{x_0} + 1]- y[{x_0}]) \cdot (x - {x_0})
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="291" BORDER="0"
 SRC="|."$dir".q|img745.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.12.ps}\end{figure}">|; 

$key = q/Q=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$Q=-1$">|; 

$key = q/{displaymath}(2,1),(4.75,0),(7.5,1),(10.25,0),(13,1),ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img319.png"
 ALT="\begin{displaymath}
(2, 1), (4.75, 0), (7.5, 1), (10.25, 0), (13, 1), \ldots
\end{displaymath}">|; 

$key = q/beta=2pislash10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="$\beta =2\pi /10$">|; 

$key = q/{c_1}+cdots+{c_l}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1300.png"
 ALT="${c_1} + \cdots + {c_l} = 0$">|; 

$key = q/-i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img949.png"
 ALT="$-i$">|; 

$key = q/{displaymath}H(Z)={{{overline{P}-{Z^{-1}}}}over{{1-P{Z^{-1}}}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img983.png"
 ALT="\begin{displaymath}
H(Z) = {{
{\overline{P} - {Z^{-1}}}
} \over {
{1 - P{Z^{-1}}}
}}
\end{displaymath}">|; 

$key = q/{displaymath}mathrm{re}(A{Z^n})=acdotcos(nomega+phi){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img662.png"
 ALT="\begin{displaymath}
\mathrm{re}(A{Z^n}) = a \cdot \cos(n \omega + \phi)
\end{displaymath}">|; 

$key = q/3pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$3\pi /2$">|; 

$key = q/NslashM;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img191.png"
 ALT="$N/M$">|; 

$key = q/{displaymath}d=20cdot{{{log}_{10}}({aslash{a_0}})}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="\begin{displaymath}
d = 20 \cdot {{{\log}_{10}} ( {a / {a_0}} )}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig05.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="480" HEIGHT="265" BORDER="0"
 SRC="|."$dir".q|img534.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.15.ps}\end{figure}">|; 

$key = q/Nslash2+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1220.png"
 ALT="$N/2+1$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="388" BORDER="0"
 SRC="|."$dir".q|img372.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.09.ps}\end{figure}">|; 

$key = q/(M,c);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="$(M, c)$">|; 

$key = q/x[n+1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img784.png"
 ALT="$x[n+1]$">|; 

$key = q/{displaymath}cos(phi)+isin(phi)=R(cos(omega)+isin(omega)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img946.png"
 ALT="\begin{displaymath}
\cos(\phi) + i \sin(\phi) = R(\cos(\omega) + i \sin(\omega))
\end{displaymath}">|; 

$key = q/N+M-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$N+M-1$">|; 

$key = q/1,W,{W^2},ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img998.png"
 ALT="$1, W, {W^2}, \ldots$">|; 

$key = q/mathrm{fft}sim;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1214.png"
 ALT="$\mathrm{fft}\sim$">|; 

$key = q/f=x-{x_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img257.png"
 ALT="$f = x - {x_0}$">|; 

$key = q/{displaymath}U=cos(omega)+isin(omega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1049.png"
 ALT="\begin{displaymath}
U = \cos(\omega) + i \sin(\omega)
\end{displaymath}">|; 

$key = q/Z=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img941.png"
 ALT="$Z=1$">|; 

$key = q/fbox{{*sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="\fbox{ $*\sim$ }">|; 

$key = q/{displaymath}omega_c+momega_m{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|img479.png"
 ALT="\begin{displaymath}
\omega_c + m \omega_m
\end{displaymath}">|; 

$key = q/Rslashf;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img809.png"
 ALT="$R/f$">|; 

$key = q/H=Nslash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1154.png"
 ALT="$H=N/4$">|; 

$key = q/Nslash4M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1362.png"
 ALT="$N/4M$">|; 

$key = q/r=0.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="$r=0.5$">|; 

$key = q/RslashB;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img320.png"
 ALT="$R/B$">|; 

$key = q/{displaymath}h[n]=12{{log_2}left|y[n]-y[n-1]right|}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img201.png"
 ALT="\begin{displaymath}
h[n] = 12 {{\log_2} \left \vert y[n] - y[n-1] \right \vert}
\end{displaymath}">|; 

$key = q/{displaymath}{f_1}={f_0},2{f_2}={f_1},3{f_3}={f_2},ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img513.png"
 ALT="\begin{displaymath}
{f_1} = {f_0} , 2 {f_2} = {f_1}, 3 {f_3} = {f_2} , \ldots
\end{displaymath}">|; 

$key = q/{displaymath}angle({U^k})=kangle(U)=komega{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1052.png"
 ALT="\begin{displaymath}
\angle({U^k}) = k \angle(U) = k\omega
\end{displaymath}">|; 

$key = q/Z^n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img653.png"
 ALT="$Z^n$">|; 

$key = q/{displaymath}{piover2}({1overn}-1),;{piover2}({3overn}-1),;ldots,;{piover2}({{2n-1}overn}-1){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img932.png"
 ALT="\begin{displaymath}
{\pi \over 2} ({1 \over n} - 1) , \;
{\pi \over 2} ({3 \ov...
...} - 1) , \; \ldots , \;
{\pi \over 2} ({{2n-1} \over n} - 1)
\end{displaymath}">|; 

$key = q/2a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$2a$">|; 

$key = q/2pislashH;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1183.png"
 ALT="$2\pi/H$">|; 

$key = q/{displaymath}cdotslet[0]let[1]let[2]lecdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="186" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img316.png"
 ALT="\begin{displaymath}
\cdots \le t[0] \le t[1] \le t[2] \le \cdots
\end{displaymath}">|; 

$key = q/B=4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img312.png"
 ALT="$B=4$">|; 

$key = q/fbox{{mathrm{del}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img338.png"
 ALT="\fbox{ $\mathrm{del}$ }">|; 

$key = q/{displaymath}{P_k}[n]={A_k}{{left[{U^k}right]}^{n}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1050.png"
 ALT="\begin{displaymath}
{P_k}[n] = {A_k}{{\left [ {U^k} \right ]} ^ {n}}
\end{displaymath}">|; 

$key = q/{displaymath}-{{{d_1}+cdots+{d_j}}over{N}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1290.png"
 ALT="\begin{displaymath}
-{{{d_1} + \cdots + {d_j}} \over {N}}
\end{displaymath}">|; 

$key = q/S(1)=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img954.png"
 ALT="$S(1) = 1$">|; 

$key = q/2pikslashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1046.png"
 ALT="$2\pi k / N$">|; 

$key = q/{displaymath}P(x[n])=left[{{|x[0]|}^2}+{{|x[1]|}^2}+cdots+{{|x[N-1]|}^2}right]slashN{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="34" BORDER="0"
 SRC="|."$dir".q|img738.png"
 ALT="\begin{displaymath}
P(x[n]) = \left [{{\vert x[0]\vert}^2} + {{\vert x[1]\vert}^2} + \cdots
+ {{\vert x[N-1]\vert}^2} \right ] / N
\end{displaymath}">|; 

$key = q/20{log_{10}}(g);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img776.png"
 ALT="$20 {\log_{10}} (g)$">|; 

$key = q/fbox{texttt{switch~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img834.png"
 ALT="\fbox{ \texttt{switch\&nbsp;}}">|; 

$key = q/{displaymath}a=cos({{pi}over4}-{{omega}over2}),;b=sin({{pi}over4}-{{omega}over2}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="227" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img962.png"
 ALT="\begin{displaymath}
a = \cos({{\pi}\over 4} - {{\omega} \over 2}) , \;
b = \sin({{\pi}\over 4} - {{\omega} \over 2})
\end{displaymath}">|; 

$key = q/Nslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1265.png"
 ALT="$N/2$">|; 

$key = q/{displaymath}{mathrm{COV}}{x[n],y[n]}={{x[M]y[M]+cdots+x[M+N-1]y[M+N-1]}overN}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="454" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="\begin{displaymath}
{\mathrm{COV}} \{ x[n] , y[n] \} =
{
{x[M]y[M] + \cdots + x[M+N-1]y[M+N-1]}
\over
N
}
\end{displaymath}">|; 

$key = q/a=;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img524.png"
 ALT="$a=$">|; 

$key = q/k=0,1,ldots,N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1147.png"
 ALT="$k = 0, 1, \ldots, N-1$">|; 

$key = q/Y[k]slashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1072.png"
 ALT="$Y[k]/N$">|; 

$key = q/fbox{{mathrm{rpole}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1033.png"
 ALT="\fbox{$\mathrm{rpole}\sim$}">|; 

$key = q/{displaymath}f={{omegaR}over{2pi}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="\begin{displaymath}
f = {{\omega R} \over {2 \pi}}
\end{displaymath}">|; 

$key = q/{displaymath}s[n]approx{1overpi}left[{sin(omegan)}+{{sin(2omegan)}over2}+{{sin(3omegan)}over3}+cdotsright]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1325.png"
 ALT="\begin{displaymath}
s[n] \approx {1 \over \pi} \left [
{\sin ( \omega n )}
+ ...
...\over 2}
+ {{\sin ( 3 \omega n)} \over 3}
+ \cdots
\right ]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig06.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="478" HEIGHT="689" BORDER="0"
 SRC="|."$dir".q|img599.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.08.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="316" HEIGHT="353" BORDER="0"
 SRC="|."$dir".q|img190.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.04.ps}\end{figure}">|; 

$key = q/c,s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img749.png"
 ALT="$c, s$">|; 

$key = q/fbox{{mathrm{tabsend}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1234.png"
 ALT="\fbox{$\mathrm{tabsend}\sim$}">|; 

$key = q/{f_3}=1slash6;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img517.png"
 ALT="${f_3}=1/6$">|; 

$key = q/{displaymath}R[k];=;{{overline{T[k]};cdot;{S[m-1,k]}}over{left|{S[m-1,k]}right|}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1205.png"
 ALT="\begin{displaymath}
R[k] \; = \;
{
{
\overline {T[k]} \; \cdot \; {S[m-1, k]}
} \over {
\left \vert
{S[m-1, k]}
\right \vert
}
}
\end{displaymath}">|; 

$key = q/|R(Z)|=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img940.png"
 ALT="$\vert R(Z)\vert = 1$">|; 

$key = q/{displaymath}x[t+tau]+y[t+tau]=x[t]+y[t]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img446.png"
 ALT="\begin{displaymath}
x[t + \tau] + y[t+\tau] = x[t] + y[t]
\end{displaymath}">|; 

$key = q/omegan+phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="$\omega n + \phi$">|; 

$key = q/{displaymath}-{{left[{{aZ+b}over{bZ+a}}right]}^2}=W{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img968.png"
 ALT="\begin{displaymath}
- {
{ \left [ {
{
aZ + b
} \over {
bZ + a
}
} \right ] }
^ 2
} = W
\end{displaymath}">|; 

$key = q/{displaymath}cos(a)-cos(b)=2sin({{b-a}over2})sin({{a+b}over2}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1352.png"
 ALT="\begin{displaymath}
\cos(a) - \cos(b) = 2 \sin({{b-a}\over 2}) \sin({{a+b}\over 2})
\end{displaymath}">|; 

$key = q/{m_a};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img560.png"
 ALT="${m_a}$">|; 

$key = q/{displaymath}x[n]={{underbrace{gleft(asin(omeganslash2)right)}_{mathrm{modulatoros(komegan)+qcos((k+1)omegan)}right]}_mathrm{carrier}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="369" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img598.png"
 ALT="\begin{displaymath}
x[n] = {
{\underbrace
{g \left ( a \sin (\omega n/2) \ri...
...) + q \cos( (k+1) \omega n)}
\right ] } _\mathrm{carrier}}
}
\end{displaymath}">|; 

$key = q/t;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$t$">|; 

$key = q/c=cos(theta);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img772.png"
 ALT="$c = \cos(\theta)$">|; 

$key = q/{displaymath}|H(cos(omega)+isin(omega))|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img938.png"
 ALT="\begin{displaymath}
\vert H(\cos(\omega) + i \sin(\omega)) \vert
\end{displaymath}">|; 

$key = q/Rt=n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$Rt = n$">|; 

$key = q/{displaymath}f(-x)=f(x){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img461.png"
 ALT="\begin{displaymath}
f(-x) = f(x)
\end{displaymath}">|; 

$key = q/d[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img787.png"
 ALT="$d[n]$">|; 

$key = q/|P|<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img883.png"
 ALT="$\vert P\vert &lt; 1$">|; 

$key = q/A_k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1054.png"
 ALT="$A_k$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="537" HEIGHT="244" BORDER="0"
 SRC="|."$dir".q|img923.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.15.ps}\end{figure}">|; 

$key = q/{displaymath}c=cos(theta){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img750.png"
 ALT="\begin{displaymath}
c = \cos(\theta)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="219" BORDER="0"
 SRC="|."$dir".q|img679.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.03.ps}\end{figure}">|; 

$key = q/{J_k}(a);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img530.png"
 ALT="${J_k}(a)$">|; 

$key = q/kslashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1304.png"
 ALT="$k/N$">|; 

$key = q/c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img293.png"
 ALT="$c$">|; 

$key = q/J(Z)=infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img965.png"
 ALT="$J(Z)=\infty$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.21.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="562" HEIGHT="630" BORDER="0"
 SRC="|."$dir".q|img394.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.21.ps}\end{figure}">|; 

$key = q/kmtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img483.png"
 ALT="$km\tau$">|; 

$key = q/1slash{k^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="$1/{k^2}$">|; 

$key = q/fbox{{mathrm{lrshift}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1242.png"
 ALT="\fbox{$\mathrm{lrshift}\sim$}">|; 

$key = q/fbox{{mathrm{r}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="\fbox{ $ \mathrm{r} $}">|; 

$key = q/C[m-2];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1162.png"
 ALT="$C[m-2]$">|; 

$key = q/3.999ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img332.png"
 ALT="$3.999\ldots$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.32.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="548" HEIGHT="276" BORDER="0"
 SRC="|."$dir".q|img1027.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.32.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{wrap}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img288.png"
 ALT="\fbox{$\mathrm{wrap}\sim$}">|; 

$key = q/k=100;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1093.png"
 ALT="$k=100$">|; 

$key = q/s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img208.png"
 ALT="$s$">|; 

$key = q/{displaymath}H(Z)={{1}over{1-P{Z^{-1}}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img882.png"
 ALT="\begin{displaymath}
H(Z) = {{1} \over {1 - P {Z^{-1}}}}
\end{displaymath}">|; 

$key = q/{displaymath}|Z|=sqrt{({a^2}+{b^2})}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img631.png"
 ALT="\begin{displaymath}
\vert Z\vert = \sqrt {({a^2} + {b^2})}
\end{displaymath}">|; 

$key = q/S(-1)=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img955.png"
 ALT="$S(-1) = -1$">|; 

$key = q/fbox{{mathrm{czero}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1037.png"
 ALT="\fbox{$\mathrm{czero}\sim$}">|; 

$key = q/{Z^{-dslash2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img692.png"
 ALT="${Z^{-d/2}}$">|; 

$key = q/{displaymath}X''[n]={{X[n]-X[-n]}over{2i}}=A[1]sin(omegan)+cdots+A[N-1]sin(omega(N-1)n){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="496" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1274.png"
 ALT="\begin{displaymath}
X''[n] = {{X[n] - X[-n]}\over {2i}} =
A[1]\sin(\omega n)+ \cdots + A[N-1]\sin(\omega (N-1) n)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig03.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="528" HEIGHT="422" BORDER="0"
 SRC="|."$dir".q|img347.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.14.ps}\end{figure}">|; 

$key = q/{J_3}(a){J_k}(b);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img547.png"
 ALT="${J_3}(a) {J_k}(b)$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.31.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="585" HEIGHT="811" BORDER="0"
 SRC="|."$dir".q|img846.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.31.ps}\end{figure}">|; 

$key = q/{displaymath}{H_1}(Z)+i{H_2}(Z)approxleft{array{{ll}2{H_1}(Z)&{0<angle(Z)<pi}0&mbox{otherwise}array{right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1013.png"
 ALT="\begin{displaymath}
{H_1}(Z) + i {H_2}(Z) \approx
\left \{
\begin{array}{ll}
...
...ngle(Z) &lt; \pi} \\\\
0 &amp; \mbox{otherwise}
\end{array} \right .
\end{displaymath}">|; 

$key = q/d_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img801.png"
 ALT="$d_0$">|; 

$key = q/{displaymath}overline{A+B}=overline{A}+overline{B}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="25" BORDER="0"
 SRC="|."$dir".q|img895.png"
 ALT="\begin{displaymath}
\overline{A+B} = \overline{A} + \overline{B}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig03.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="51" BORDER="0"
 SRC="|."$dir".q|img314.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.03.ps}\end{figure}">|; 

$key = q/({a^2}+{b^2})slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img996.png"
 ALT="$({a^2} +
{b^2})/2$">|; 

$key = q/fbox{{mathrm{inlet}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img374.png"
 ALT="\fbox{ $ \mathrm{inlet} $}">|; 

$key = q/{displaymath}={2overpi}left[{sin(omegan)}+{{sin(3omegan)}over3}+{{sin(5omegan)}over5}+cdotsright]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="300" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1339.png"
 ALT="\begin{displaymath}
= {2 \over \pi} \left [
{\sin ( \omega n )}
+ {{\sin ( 3 ...
...\over 3}
+ {{\sin ( 5 \omega n)} \over 5}
+ \cdots
\right ]
\end{displaymath}">|; 

$key = q/Halpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1180.png"
 ALT="$H\alpha$">|; 

$key = q/a=2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="$a=2$">|; 

$key = q/{displaymath}X[n]={Z^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img684.png"
 ALT="\begin{displaymath}
X[n] = {Z^n}
\end{displaymath}">|; 

$key = q/{displaymath}{{left({A_{mathrm{RMS}}}{x[n]+y[n]}right)}^2}={{left({A_{mathrm{RMSn]}right)}^2}+{{left({A_{mathrm{RMS}}}{y[n]}right)}^2}.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="398" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="\begin{displaymath}
{{\left ( {A_{\mathrm{RMS}}} \{x[n]+y[n]\} \right ) } ^ 2} ...
...2} +
{{\left ( {A_{\mathrm{RMS}}} \{y[n]\} \right ) } ^ 2} .
\end{displaymath}">|; 

$key = q/1slashoverline{Q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img907.png"
 ALT="$1/\overline{Q}$">|; 

$key = q/W;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="$W$">|; 

$key = q/{figure}vspace*{-15pt}{centerline{psfig{file=figsslashfig06.11.ps,width=3.8in}}{vspace*{-13pt}{{vspace*{13pt}{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="235" BORDER="0"
 SRC="|."$dir".q|img609.png"
 ALT="\begin{figure}\vspace*{-15pt}
\centerline{\psfig{file=figs/fig06.11.ps,width=3.8in}}
\vspace*{-13pt}\vspace*{13pt}
\end{figure}">|; 

$key = q/Q_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img898.png"
 ALT="$Q_i$">|; 

$key = q/fbox{{mathrm{receive}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="88" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img291.png"
 ALT="\fbox{ $\mathrm{receive}\sim$ }">|; 

$key = q/{figure}{psfig{file=figsslashfig09.17.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="596" HEIGHT="523" BORDER="0"
 SRC="|."$dir".q|img1236.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.17.ps}\end{figure}">|; 

$key = q/pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="$\pi $">|; 

$key = q/{displaymath}Z=rcdotleft[cos(theta)+isin(theta)right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img638.png"
 ALT="\begin{displaymath}
Z = r \cdot \left[ \cos(\theta) + i \sin(\theta) \right ]
\end{displaymath}">|; 

$key = q/fbox{texttt{throw~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img388.png"
 ALT="\fbox{ \texttt{throw\&nbsp;}}">|; 

$key = q/{displaymath}<comment_mark>127{f_2}(x)=10^{2(x-1)}hspace{0.2in}mathrm{(dBtolinear),}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img362.png"
 ALT="\begin{displaymath}
       %
{f_2} (x) = 10^{2(x-1)} \hspace{0.2in}\mathrm{(dB to linear),}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig01.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="404" HEIGHT="172" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.15.ps}\end{figure}">|; 

$key = q/f=261.626;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$f=261.626$">|; 

$key = q/s[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1311.png"
 ALT="$s[n]$">|; 

$key = q/overline{Z}={Z^{-1}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img877.png"
 ALT="$\overline{Z} = {Z^{-1}}$">|; 

$key = q/{displaymath}{A_{mathrm{peak}}}{x[n]}=max|x[n]|,hspace{0.3in}n=M,ldots,M+N-1{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="\begin{displaymath}
{A_{\mathrm{peak}}} \{x[n]\} = \max \vert x[n] \vert ,
\hspace{0.3in}n = M, \ldots, M+N-1
\end{displaymath}">|; 

$key = q/(n+f,y);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img323.png"
 ALT="$(n+f, y)$">|; 

$key = q/fbox{{mathrm{dac}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="\fbox{ $ \mathrm{dac}\sim $}">|; 

$key = q/pislashomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img226.png"
 ALT="$\pi / \omega$">|; 

$key = q/lfloory[n]rfloor;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$\lfloor y[n] \rfloor$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.29.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="465" HEIGHT="376" BORDER="0"
 SRC="|."$dir".q|img838.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.29.ps}\end{figure}">|; 

$key = q/fbox{texttt{czero_rev~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1035.png"
 ALT="\fbox{ \texttt{czero\_rev\&nbsp;}}">|; 

$key = q/t_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="$t_2$">|; 

$key = q/{displaymath}{1overN}left[{calFT}{s[n]}(1)cdot{U^n}+{calFT}{s[n]}(-1)cdot{U^{-n}}right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1321.png"
 ALT="\begin{displaymath}
{1 \over N}\left [
{\cal FT}\{ s[n] \} (1) \cdot {U^n} +
{\cal FT}\{ s[n] \} (-1) \cdot {U^{-n}}
\right ]
\end{displaymath}">|; 

$key = q/{displaymath}|H|=2|cos(omegadslash2)|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img701.png"
 ALT="\begin{displaymath}
\vert H\vert = 2 \vert\cos(\omega d / 2) \vert
\end{displaymath}">|; 

$key = q/V;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1059.png"
 ALT="$V$">|; 

$key = q/z[n]=x[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img204.png"
 ALT="$z[n] = x[n]$">|; 

$key = q/{figure}{psfig{file=figsslashfig02.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="317" BORDER="0"
 SRC="|."$dir".q|img242.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.10.ps}\end{figure}">|; 

$key = q/{displaymath}p[n]-p[n-1]={{{{({noverN}-{1over2})}^2}-{{({{n-1}overN}-{1over2})}^2}}over{2}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="285" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img1326.png"
 ALT="\begin{displaymath}
p[n] - p[n-1] = {
{
{{({n\over N} - {1\over 2})}^2} -
{{({{n-1}\over N} - {1\over 2})}^2}
} \over {
2
}}
\end{displaymath}">|; 

$key = q/{P_1},ldots,{P_k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img888.png"
 ALT="${P_1}, \ldots, {P_k}$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="261" BORDER="0"
 SRC="|."$dir".q|img551.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.01.ps}\end{figure}">|; 

$key = q/{displaymath}=mathrm{re}left[{{{2-2,mathrm{re}(P){Z^{-1}}}over{(1-{P}{Z^{-1}})(1-{overline{P}}{Z^{-1}})}}{A{Z^n}}}right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img903.png"
 ALT="\begin{displaymath}
=
\mathrm{re} \left[ {
{{
2 - 2   \mathrm{re} (P) {Z^{-...
...^{-1}}) (1 - {\overline{P}}{Z^{-1}})
}}
{A{Z^n}}
} \right ]
\end{displaymath}">|; 

$key = q/fbox{{mathrm{cos}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img282.png"
 ALT="\fbox{ $\mathrm{cos}\sim$ }">|; 

$key = q/{displaymath}Halpha=angleS[1,3]-angleS[0,3]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="169" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1181.png"
 ALT="\begin{displaymath}
H \alpha = \angle S[1, 3] - \angle S[0, 3]
\end{displaymath}">|; 

$key = q/infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img305.png"
 ALT="$\infty$">|; 

$key = q/p[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1347.png"
 ALT="$p[n]$">|; 

$key = q/1-|P|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img974.png"
 ALT="$1-\vert P\vert$">|; 

$key = q/{displaymath}-f(f-1)(f-2)slash6cdoty[{x_0}-1]+(f+1)(f-1)(f-2)slash2cdoty[{x_0}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="435" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img255.png"
 ALT="\begin{displaymath}
-f (f-1)(f-2)/6 \cdot y[{x_0}-1]
+ (f+1)(f-1)(f-2)/2 \cdot y[{x_0}]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="257" BORDER="0"
 SRC="|."$dir".q|img709.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.08.ps}\end{figure}">|; 

$key = q/{displaymath}-(f+1)f(f-2)slash2cdoty[{x_0}+1]+(f+1)f(f-1)slash6cdoty[{x_0}+2]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="422" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img256.png"
 ALT="\begin{displaymath}
- (f+1) f (f-2) / 2 \cdot y[{x_0}+1]
+ (f+1) f (f-1) / 6 \cdot y[{x_0}+2]
\end{displaymath}">|; 

$key = q/{displaymath}x[n]=cos(acos(omega_mn)+omega_cn){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img468.png"
 ALT="\begin{displaymath}
x[n] = \cos(a \cos(\omega_m n) + \omega_c n )
\end{displaymath}">|; 

$key = q/{displaymath}{1overN}{calFT}left{Y[k]right}(m)=X[-m]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="190" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1071.png"
 ALT="\begin{displaymath}
{1 \over N} {\cal FT} \left \{ Y[k] \right \} (m) = X[-m]
\end{displaymath}">|; 

$key = q/beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\beta $">|; 

$key = q/FT;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1155.png"
 ALT="$FT$">|; 

$key = q/fbox{{mathrm{t}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img355.png"
 ALT="\fbox{ $\mathrm{t}$}">|; 

$key = q/{displaymath}Phi(k)=-picdot(k-{{alpha}over{omega}})cdot(N-1)slashN{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="228" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1120.png"
 ALT="\begin{displaymath}
\Phi(k) = - \pi \cdot (k - {{\alpha } \over {\omega}}) \cdot (N-1)/N
\end{displaymath}">|; 

$key = q/{displaymath}f(x)={e^x}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img519.png"
 ALT="\begin{displaymath}
f(x) = {e ^ x}
\end{displaymath}">|; 

$key = q/{displaymath}={{{{{2n}over{N^2}}-{1over{N}}}+{1over{N^2}}}over{2}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img1328.png"
 ALT="\begin{displaymath}
= {
{
{{{2n}\over {N^2}} - {1\over {N}}} + {1\over {N^2}}
} \over {
2
}}
\end{displaymath}">|; 

$key = q/{displaymath}x[1.5]={{9cos(omegaslash2)-cos(3omegaslash2)}over4}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img796.png"
 ALT="\begin{displaymath}
x[1.5] = {{9 \cos(\omega/2) - \cos(3 \omega / 2)}\over4}
\end{displaymath}">|; 

$key = q/{displaymath}J(Z)=H(R(Z)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="117" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img944.png"
 ALT="\begin{displaymath}
J(Z) = H(R(Z))
\end{displaymath}">|; 

$key = q/p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$p$">|; 

$key = q/N+1-k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img258.png"
 ALT="$N + 1 - k$">|; 

$key = q/fbox{texttt{delwrite~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img819.png"
 ALT="\fbox{ \texttt{delwrite\&nbsp;}}">|; 

$key = q/1slash{sqrtN};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$1 / {\sqrt N}$">|; 

$key = q/{x_r}[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img741.png"
 ALT="${x_r}[n]$">|; 

$key = q/fbox{{mathrm{notein}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img352.png"
 ALT="\fbox{ $\mathrm{notein}$}">|; 

$key = q/overline{Q};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img872.png"
 ALT="$\overline{Q}$">|; 

$key = q/|H|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="$\vert H\vert$">|; 

$key = q/{Z_1}{Z_2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img648.png"
 ALT="${Z_1}{Z_2}$">|; 

$key = q/1slashi=-i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1318.png"
 ALT="$1/i = -i$">|; 

$key = q/{displaymath}+qcos((n+1){omega_2}t+rcos({omega_1}t)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="212" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img597.png"
 ALT="\begin{displaymath}
+ q \cos ( (n+1) {\omega_2} t + r \cos ({\omega_1} t))
\end{displaymath}">|; 

$key = q/{displaymath}{cos(alphan+phi)cos(betan+xi)}={displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img413.png"
 ALT="\begin{displaymath}
{\cos(\alpha n + \phi) \cos (\beta n + \xi)}
=
\end{displaymath}">|; 

$key = q/{displaymath}X'[n]={{X[n]+X[n+Nslash2]}over2}=A[0]+A[2]{U^{2n}}+cdots+A[N-2]{U^{(N-2)n}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1259.png"
 ALT="\begin{displaymath}
X'[n] = {{X[n] + X[n+N/2]}\over 2} =
A[0] + A[2]{U^{2n}} + \cdots + A[N-2]{U^{(N-2)n}}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="546" HEIGHT="256" BORDER="0"
 SRC="|."$dir".q|img908.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.12.ps}\end{figure}">|; 

$key = q/alpha=3omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1177.png"
 ALT="$\alpha = 3\omega$">|; 

$key = q/sslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img214.png"
 ALT="$s/2$">|; 

$key = q/{displaymath}{H_{mathrm{re}}}(Z)={{1-mathrm{re}(P){Z^{-1}}}over{(1-{P}{Z^{-1}})(1-{overline{P}}{Z^{-1}})}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="235" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img905.png"
 ALT="\begin{displaymath}
{H_{\mathrm{re}}}(Z) = {{
1 - \mathrm{re} (P) {Z^{-1}}
} \over {
(1 - {P}{Z^{-1}}) (1 - {\overline{P}}{Z^{-1}})
}}
\end{displaymath}">|; 

$key = q/1000cdot2048slashR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img839.png"
 ALT="$1000\cdot2048/R$">|; 

$key = q/omega=angle(Z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img678.png"
 ALT="$\omega = \angle(Z)$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="444" HEIGHT="680" BORDER="0"
 SRC="|."$dir".q|img1146.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.07.ps}\end{figure}">|; 

$key = q/f(x)={x^2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$f(x) = {x^2}$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="420" BORDER="0"
 SRC="|."$dir".q|img1172.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.09.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.16.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="498" HEIGHT="389" BORDER="0"
 SRC="|."$dir".q|img384.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.16.ps}\end{figure}">|; 

$key = q/{displaymath}{f_k}={1over{1cdot2cdot3cdot...cdotk}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img518.png"
 ALT="\begin{displaymath}
{f_k} = {1 \over {1 \cdot 2 \cdot 3 \cdot ... \cdot k}}
\end{displaymath}">|; 

$key = q/{displaymath}w[n]={1over2}-{1over2}cos(2pinslashN){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1125.png"
 ALT="\begin{displaymath}
w[n] = {1\over 2} - {1\over 2} \cos(2\pi n / N)
\end{displaymath}">|; 

$key = q/-1slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img212.png"
 ALT="$-1/2$">|; 

$key = q/{displaymath}z[n]=left{{array{{ll}x[lfloory[n]rfloor]&mbox{if{0ley[n]<N-1{}x[0]&mbox{if{y[n]<0{}x[N-1]&mbox{if{y[n]geN-1{}array{}right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="\begin{displaymath}
z[n] = \left \{ {
\begin{array}{ll}
x[ \lfloor y[n] \rflo...
...x[N-1] &amp; \mbox{if $y[n] \ge N-1$} \\\\
\end{array} } \right .
\end{displaymath}">|; 

$key = q/{displaymath}fx+(1-f)y,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img325.png"
 ALT="\begin{displaymath}
fx + (1-f)y,
\end{displaymath}">|; 

$key = q/|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="7" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img202.png"
 ALT="$\vert$">|; 

$key = q/1-g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img733.png"
 ALT="$1-g$">|; 

$key = q/{displaymath}R(Z)=-{Z^2}=-{{1cdot{Z^2}+0cdotZ+0}over{0cdot{Z^2}+0cdotZ+1}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="242" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img948.png"
 ALT="\begin{displaymath}
R(Z) = -{Z^2} = -
{{
1 \cdot {Z^2} + 0 \cdot Z + 0
} \over {
0 \cdot {Z^2} + 0 \cdot Z + 1
}}
\end{displaymath}">|; 

$key = q/{displaymath}={{left[{U^{0}}right]}^{n}}Y[0]+{{left[{U^{1}}right]}^{n}}Y[1]+cdots+{{left[{U^{N-1}}right]}^{n}}Y[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="360" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1075.png"
 ALT="\begin{displaymath}
= {{\left [ {U^{0}} \right ]} ^ {n}} Y[0] +
{{\left [ {U^{...
...Y[1] +
\cdots +
{{\left [ {U^{N-1}} \right ]} ^ {n}} Y[N-1]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="288" HEIGHT="226" BORDER="0"
 SRC="|."$dir".q|img857.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.04.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{rifft}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1225.png"
 ALT="\fbox{$\mathrm{rifft}\sim$}">|; 

$key = q/{displaymath}{calFT}{s[n]}(k)approx{1over{iomegak}}={{-iN}over{2pik}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1316.png"
 ALT="\begin{displaymath}
{\cal FT}\{ s[n] \} (k) \approx {1 \over {i \omega k}}
= {{-iN} \over {2 \pi k}}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig01.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="445" HEIGHT="274" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.04.ps}\end{figure}">|; 

$key = q/|Z|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img629.png"
 ALT="$\vert Z\vert$">|; 

$key = q/(L,d);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1287.png"
 ALT="$(L, d)$">|; 

$key = q/{displaymath}left.+{{cos(2omega(n-M))-cos(2omega(n+M))}over4}+cdotsright]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1351.png"
 ALT="\begin{displaymath}
\left .
+ {{\cos ( 2 \omega (n-M)) - \cos ( 2 \omega (n+M))} \over 4}
+ \cdots
\right ]
\end{displaymath}">|; 

$key = q/approx;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img549.png"
 ALT="$\approx$">|; 

$key = q/x[n]-x[n-1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1303.png"
 ALT="$x[n] - x[n-1]$">|; 

$key = q/f(x)=x^5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img496.png"
 ALT="$f(x) = x^5$">|; 

$key = q/{displaymath}{calFT}left{X[n]right}(k)={xi^{N-1}}{{{xi^N}-{xi^{-N}}}over{xi-{xi^{-1}}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1085.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ X[n] \right \} (k) =
{\xi^{N-1}}
{{
{\xi^N} - {\xi^{-N}}
} \over {
\xi - {\xi^{-1}}
}}
\end{displaymath}">|; 

$key = q/{displaymath}={calFT}left{{1over2}{Z^n}-{1over4}{(UZ)^n}-{1over4}{({U^{-1}}Z)^n}right}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1128.png"
 ALT="\begin{displaymath}
= {\cal FT} \left \{ {1\over 2} {Z^n} - {1\over 4} {(UZ)^n}
- {1\over 4} {({U^{-1}}Z)^n}\right \} (k)
\end{displaymath}">|; 

$key = q/2pikslashomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$2 \pi k/ \omega$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="339" HEIGHT="379" BORDER="0"
 SRC="|."$dir".q|img723.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.09.ps}\end{figure}">|; 

$key = q/4pislashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1043.png"
 ALT="$4\pi/N$">|; 

$key = q/{displaymath}{y_2}[n]=s{x_1}[n]+c{x_2}[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img748.png"
 ALT="\begin{displaymath}
{y_2}[n] = s {x_1}[n] + c {x_2}[n]
\end{displaymath}">|; 

$key = q/X[n]=-X[n+Nslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1266.png"
 ALT="$X[n] = -X[n+N/2$">|; 

$key = q/A[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1251.png"
 ALT="$A[k]$">|; 

$key = q/{displaymath}g(x)=e^{-x^2}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img568.png"
 ALT="\begin{displaymath}
g(x) = e ^ {- x ^ 2}
\end{displaymath}">|; 

$key = q/{displaymath}x[n]=8p[n]-8p[n-{Nover2}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1340.png"
 ALT="\begin{displaymath}
x[n] = 8 p[n] - 8 p[n-{N \over 2}]
\end{displaymath}">|; 

$key = q/40;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$40$">|; 

$key = q/n=0,ldots,N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1042.png"
 ALT="$n=0,\ldots,N-1$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="382" HEIGHT="401" BORDER="0"
 SRC="|."$dir".q|img1212.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.13.ps}\end{figure}">|; 

$key = q/{displaymath}y[t+tauslash4]=y[t]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img445.png"
 ALT="\begin{displaymath}
y[t + \tau/4] = y[t]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.31.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="506" HEIGHT="289" BORDER="0"
 SRC="|."$dir".q|img1026.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.31.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig10.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="351" BORDER="0"
 SRC="|."$dir".q|img1249.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.01.ps}\end{figure}">|; 

$key = q/{displaymath}H(overline{Z})=overline{H(Z)}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img892.png"
 ALT="\begin{displaymath}
H(\overline{Z}) = \overline{H(Z)}
\end{displaymath}">|; 

$key = q/-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img401.png"
 ALT="$-1$">|; 

$key = q/{figure}{psfig{file=figsslashfig03.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="533" BORDER="0"
 SRC="|."$dir".q|img336.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.11.ps}\end{figure}">|; 

$key = q/2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img269.png"
 ALT="$2$">|; 

$key = q/fbox{texttt{catch~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img386.png"
 ALT="\fbox{ \texttt{catch\&nbsp;}}">|; 

$key = q/{displaymath}f={{t-p}overc}={{{{2^{hslash12}}}-p}overc}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img295.png"
 ALT="\begin{displaymath}
f = {{t - p} \over c} = {{{{2 ^ {h/12}}} - p} \over c}
\end{displaymath}">|; 

$key = q/{displaymath}X[n]={A_0}{{left[{U^0}right]}^{n}}+{A_1}{{left[{U^1}right]}^{n}}+cdots+{A_{N-1}}{{left[{U^{N-1}}right]}^{n}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1053.png"
 ALT="\begin{displaymath}
X[n] =
{A_0}{{\left [ {U^0} \right ]} ^ {n}}
+ {A_1}{{\l...
...n}}
+ \cdots
+ {A_{N-1}}{{\left [ {U^{N-1}} \right ]} ^ {n}}
\end{displaymath}">|; 

$key = q/{displaymath}={{(VZ)}^{0}}X[0]+{{(VZ)}^{1}}X[1]+cdots+{{(VZ)}^{N-1}}X[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1112.png"
 ALT="\begin{displaymath}
=
{{(VZ)} ^ {0}} X[0] +
{{(VZ)} ^ {1}} X[1] +
\cdots +
{{(VZ)} ^ {N-1}} X[N-1]
\end{displaymath}">|; 

$key = q/+a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img425.png"
 ALT="$+a$">|; 

$key = q/{displaymath}b=mathrm{im}(Z){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img627.png"
 ALT="\begin{displaymath}
b = \mathrm{im}(Z)
\end{displaymath}">|; 

$key = q/sin({theta_1})sin({theta_2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img645.png"
 ALT="$\sin({\theta_1}) \sin({\theta_2})$">|; 

$key = q/p{c_1}+q{c_2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img617.png"
 ALT="$p
{c_1} + q {c_2}$">|; 

$key = q/-54;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1142.png"
 ALT="$-54$">|; 

$key = q/{displaymath}array{{lll}{angleS[0,2]=phi+pi}&{angleS[0,3]=phi}&{angleS[0,4]=phi+eS[2,3]=phi+2Halpha}&{angleS[2,4]=phi+2Halpha+pi}array{{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="494" HEIGHT="64" BORDER="0"
 SRC="|."$dir".q|img1179.png"
 ALT="\begin{displaymath}
\begin{array}{lll}
{\angle S[0, 2] = \phi + \pi} &amp;
{\angl...
...ha} &amp;
{\angle S[2, 4] = \phi + 2H\alpha + \pi}\\\\
\end{array}\end{displaymath}">|; 

$key = q/685600slash440=1558;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1368.png"
 ALT="$685600/440=1558$">|; 

$key = q/fbox{{mathrm{r}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img292.png"
 ALT="\fbox{ $\mathrm{r}\sim$ }">|; 

$key = q/{calFT}left{X[n]right}(k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1095.png"
 ALT="${\cal FT} \left \{ X[n] \right \} (k)$">|; 

$key = q/{displaymath}M(k)={left[{{1over2}{D_N}(k)+{1over4}{D_N}(k+1)+{1over4}{D_N}(k-1)}right]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="340" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1131.png"
 ALT="\begin{displaymath}
M(k) =
{\left [ {
{1\over 2}{D_N}(k)
+ {1\over 4}{D_N}(k + 1)
+ {1\over 4}{D_N}(k - 1)
} \right ] }
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="325" HEIGHT="440" BORDER="0"
 SRC="|."$dir".q|img219.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.07.ps}\end{figure}">|; 

$key = q/{displaymath}Y[n]=X[n-d]=A{Z^{(n-d)}}={Z^{-d}}A{Z^n}={Z^{-d}}X[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img675.png"
 ALT="\begin{displaymath}
Y[n] = X[n-d] = A {Z^{(n-d)}} = {Z^{-d}} A {Z^n} = {Z^{-d}} X[n]
\end{displaymath}">|; 

$key = q/{displaymath}{Z^n}+{Z^{-d}}{Z^n}=(1+{Z^{-d}}){Z^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="200" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img686.png"
 ALT="\begin{displaymath}
{Z^n} + {Z^{-d}} {Z^n} = (1 + {Z^{-d}}) {Z^n}
\end{displaymath}">|; 

$key = q/-pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img283.png"
 ALT="$-\pi/2$">|; 

$key = q/fbox{{mathrm{czero_rev}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1038.png"
 ALT="\fbox{$\mathrm{czero\_rev}\sim$}">|; 

$key = q/fbox{{mathrm{vline}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img346.png"
 ALT="\fbox{ $\mathrm{vline}\sim$}">|; 

$key = q/1slashe;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img980.png"
 ALT="$1/e$">|; 

$key = q/{displaymath}ldots,t[0],t[1],t[2],ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="133" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img315.png"
 ALT="\begin{displaymath}
\ldots , t[0], t[1], t[2], \ldots
\end{displaymath}">|; 

$key = q/{displaymath}mathrm{RT}={{-3d}over{{log_{10}}(g)}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img779.png"
 ALT="\begin{displaymath}
\mathrm{RT} = {{-3d} \over {{\log_{10}}(g) }}
\end{displaymath}">|; 

$key = q/f(x)=cos(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img473.png"
 ALT="$f(x) = \cos(x)$">|; 

$key = q/{displaymath}{x_{50}}[n]={b_0}+{b_1}cosleft(omegan+{theta_1}right)+{b_2}cosleft(2omegan+{theta_2}right)+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="373" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img227.png"
 ALT="\begin{displaymath}
{x_{50}}[n] = {b_0} +
{b_1} \cos \left ( \omega n + {\thet...
...
{b_2} \cos \left ( 2 \omega n + {\theta_2} \right ) + \cdots
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.33.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="484" HEIGHT="421" BORDER="0"
 SRC="|."$dir".q|img1040.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.33.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{receive}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="\fbox{ $ \mathrm{receive} $}">|; 

$key = q/{displaymath}x[n]=cos(omega_cn+acos(omega_mn)+bcos(omega_pn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img542.png"
 ALT="\begin{displaymath}
x[n] = \cos(\omega_c n + a \cos(\omega_m n) + b \cos(\omega_p n))
\end{displaymath}">|; 

$key = q/fbox{texttt{fiddle~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img488.png"
 ALT="\fbox{ \texttt{fiddle\&nbsp;}}">|; 

$key = q/t=nslashR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$t = n/R$">|; 

$key = q/alpha=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="$\alpha =0$">|; 

$key = q/{displaymath}X[n]+Y[n]=(A+B){Z^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="181" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img666.png"
 ALT="\begin{displaymath}
X[n] + Y[n] = (A+B) {Z^n}
\end{displaymath}">|; 

$key = q/e^x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img521.png"
 ALT="$e^x$">|; 

$key = q/1,WZ,{{(WZ)}^2},ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img999.png"
 ALT="$1, WZ, {{(WZ)}^2}, \ldots$">|; 

$key = q/{displaymath}{x^4}[n]={1over8}cos(-2omegan)+{3over8}cos(0)+{3over8}cos(2omegan)+{1over8}cos(4omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img456.png"
 ALT="\begin{displaymath}
{x^4}[n] = {1 \over 8} \cos (-2\omega n) + {3 \over 8} \cos...
... {3 \over 8} \cos (2 \omega n) + {1 \over 8} \cos (4 \omega n)
\end{displaymath}">|; 

$key = q/R(Z)=-Z^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img952.png"
 ALT="$R(Z) = -Z^2$">|; 

$key = q/{displaymath}={V^{0}}X[0]+{V^{1}}ZX[1]+cdots+{V^{N-1}}{Z^{N-1}}X[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1111.png"
 ALT="\begin{displaymath}
=
{V ^ {0}} X[0] +
{V ^ {1}} Z X[1] +
\cdots +
{V ^ {N-1}} {Z^{N-1}} X[N-1]
\end{displaymath}">|; 

$key = q/fbox{{mathrm{outlet}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img376.png"
 ALT="\fbox{ $\mathrm{outlet}$ }">|; 

$key = q/-pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img576.png"
 ALT="$-\pi$">|; 

$key = q/omega=phi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img410.png"
 ALT="$\omega = \phi = 0$">|; 

$key = q/1slash(1-p);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img909.png"
 ALT="$1/(1-p)$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.24.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="387" BORDER="0"
 SRC="|."$dir".q|img986.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.24.ps}\end{figure}">|; 

$key = q/{displaymath}f(n)=1,,,,,,,n=,,ldots,-1,0,1,ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img298.png"
 ALT="\begin{displaymath}
f(n) = 1   ,           n =     \ldots, -1, 0, 1, \ldots
\end{displaymath}">|; 

$key = q/d=omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img915.png"
 ALT="$d = \omega$">|; 

$key = q/P_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img899.png"
 ALT="$P_i$">|; 

$key = q/fbox{{mathrm{send}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img158.png"
 ALT="\fbox{ $\mathrm{send}$}">|; 

$key = q/{figure}{psfig{file=figsslashfig05.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="234" HEIGHT="171" BORDER="0"
 SRC="|."$dir".q|img532.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.14.ps}\end{figure}">|; 

$key = q/phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="$\phi$">|; 

$key = q/{displaymath}20{mathrm{RT}overd}{log_{10}}(g)=-60{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="144" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img778.png"
 ALT="\begin{displaymath}
20 {\mathrm{RT}\over d} {\log_{10}}( g ) = -60
\end{displaymath}">|; 

$key = q/{displaymath}{H_1}(Z)approxi{H_2}(Z),;0<angle(Z)<pi{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="221" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1009.png"
 ALT="\begin{displaymath}
{H_1}(Z) \approx i {H_2}(Z) , \; 0 &lt; \angle(Z) &lt; \pi
\end{displaymath}">|; 

$key = q/n=5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img978.png"
 ALT="$n=5$">|; 

$key = q/fbox{texttt{noise~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1019.png"
 ALT="\fbox{ \texttt{noise\&nbsp;}}">|; 

$key = q/fbox{{mathrm{bang}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1232.png"
 ALT="\fbox{$\mathrm{bang}\sim$}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="217" HEIGHT="153" BORDER="0"
 SRC="|."$dir".q|img380.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.13.ps}\end{figure}">|; 

$key = q/{displaymath}{calFT}{x[n-1]}=left[cos(komega)-isin(komega)right]{calFT}{x[n]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="329" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1305.png"
 ALT="\begin{displaymath}
{\cal FT}\{ x[n-1] \} =
\left [ \cos(k \omega) - i \sin (k \omega) \right ]
{\cal FT}\{ x[n] \}
\end{displaymath}">|; 

$key = q/-pilephilepi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img556.png"
 ALT="$-\pi \le \phi \le \pi$">|; 

$key = q/{displaymath}=(cos(omegadslash2)+isin(omegadslash2))+(cos(omegadslash2)-isin(omegadslash2)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="384" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img699.png"
 ALT="\begin{displaymath}
= (\cos(\omega d / 2) + i \sin(\omega d / 2)) +
(\cos(\omega d / 2) - i \sin(\omega d / 2))
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig10.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="477" HEIGHT="467" BORDER="0"
 SRC="|."$dir".q|img1277.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.02.ps}\end{figure}">|; 

$key = q/mH;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1149.png"
 ALT="$mH$">|; 

$key = q/{figure}{psfig{file=figsslashfig02.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="427" HEIGHT="346" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.03.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.16.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="449" HEIGHT="484" BORDER="0"
 SRC="|."$dir".q|img780.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.16.ps}\end{figure}">|; 

$key = q/1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img262.png"
 ALT="$1$">|; 

$key = q/alpha=pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img933.png"
 ALT="$\alpha = \pi/2$">|; 

$key = q/{displaymath}x(phi)=T(cphi)*W(aphi),{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img555.png"
 ALT="\begin{displaymath}
x(\phi) = T (c \phi) * W (a \phi),
\end{displaymath}">|; 

$key = q/mH+n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1150.png"
 ALT="$mH+n$">|; 

$key = q/w;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img770.png"
 ALT="$w$">|; 

$key = q/{displaymath}Y=XZ{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="24" BORDER="0"
 SRC="|."$dir".q|img757.png"
 ALT="\begin{displaymath}
Y = XZ
\end{displaymath}">|; 

$key = q/{displaymath}{{x[n]}^2}={{a^2}over2}left(cos(2alphan)+1right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img992.png"
 ALT="\begin{displaymath}
{{x[n]}^2} = {{a^2}\over 2} \left ( \cos(2 \alpha n) + 1 \right )
\end{displaymath}">|; 

$key = q/{displaymath}AcdotH(Z)cdot{Z^n}+overline{A}cdotoverline{H(Z)}cdot{{overline{Z}}^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img894.png"
 ALT="\begin{displaymath}
A \cdot H(Z) \cdot {Z^n} +
\overline{A} \cdot \overline{H(Z)} \cdot {{\overline{Z}}^n}
\end{displaymath}">|; 

$key = q/16cdot44100=705600;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1366.png"
 ALT="$16\cdot 44100 =
705600$">|; 

$key = q/S[m,k]=C[m];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1165.png"
 ALT="$S[m, k] = C[m]$">|; 

$key = q/{displaymath}cos(6omegan){M_a}(omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img581.png"
 ALT="\begin{displaymath}
\cos(6 \omega n) {M_a}(\omega n)
\end{displaymath}">|; 

$key = q/{displaymath}x[n+1]-x[n]={foverR}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img811.png"
 ALT="\begin{displaymath}
x[n+1] - x[n] = {f \over R}
\end{displaymath}">|; 

$key = q/m[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1229.png"
 ALT="$m[k]$">|; 

$key = q/a=|T'[k]|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1193.png"
 ALT="$a = \vert T'[k]\vert$">|; 

$key = q/(0,ldots,0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img742.png"
 ALT="$(0, \ldots, 0)$">|; 

$key = q/|U|=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img943.png"
 ALT="$\vert U\vert=1$">|; 

$key = q/fbox{{mathrm{loadbang}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img286.png"
 ALT="\fbox{ $\mathrm{loadbang}$ }">|; 

$key = q/{displaymath}beta*(beta+2omega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="84" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img924.png"
 ALT="\begin{displaymath}
\beta * (\beta + 2 \omega)
\end{displaymath}">|; 

$key = q/{displaymath}f(x)={f_0}+{f_1}x+{f_2}{x^2}+{f_3}{x^3}+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img449.png"
 ALT="\begin{displaymath}
f(x) = {f_0} + {f_1}x + {f_2}{x^2} + {f_3}{x^3} + \cdots
\end{displaymath}">|; 

$key = q/{displaymath}{Z_2}={r_2}cdotleft[cos({theta_2})+isin({theta_2})right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img642.png"
 ALT="\begin{displaymath}
{Z_2} = {r_2} \cdot \left [ \cos({\theta_2}) + i \sin({\theta_2}) \right ]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig10.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="617" HEIGHT="359" BORDER="0"
 SRC="|."$dir".q|img1377.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.14.ps}\end{figure}">|; 

$key = q/P=Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img886.png"
 ALT="$P=Q$">|; 

$key = q/{displaymath}T'[k]={calFT}(W(n)X[n+H])(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="219" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1189.png"
 ALT="\begin{displaymath}
T'[k] = {\cal FT}(W(n)X[n+H]) (k)
\end{displaymath}">|; 

$key = q/1slash100;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img364.png"
 ALT="$1/100$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="227" BORDER="0"
 SRC="|."$dir".q|img367.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.04.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig06.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="488" HEIGHT="675" BORDER="0"
 SRC="|."$dir".q|img584.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.06.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig09.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="459" HEIGHT="405" BORDER="0"
 SRC="|."$dir".q|img1186.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.11.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="353" HEIGHT="134" BORDER="0"
 SRC="|."$dir".q|img378.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.11.ps}\end{figure}">|; 

$key = q/{displaymath}beta=2arctan(r){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img935.png"
 ALT="\begin{displaymath}
\beta = 2 \arctan (r)
\end{displaymath}">|; 

$key = q/p=1-beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img919.png"
 ALT="$p = 1 - \beta$">|; 

$key = q/{displaymath}{{1}over{1-P{Z^{-1}}}}{Z^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img881.png"
 ALT="\begin{displaymath}
{{1} \over {1 - P {Z^{-1}}}} {Z^n}
\end{displaymath}">|; 

$key = q/omega=pislash10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="$\omega = \pi/10$">|; 

$key = q/Z^d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img693.png"
 ALT="$Z^d$">|; 

$key = q/f[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1167.png"
 ALT="$f[k]$">|; 

$key = q/{displaymath}a[k]={1over{{pi^2}(MslashN-2{{(MslashN)}^2})}}cdot{{sin(2pikMslashN)}over{k^2}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="47" BORDER="0"
 SRC="|."$dir".q|img1355.png"
 ALT="\begin{displaymath}
a[k] = {1 \over {{\pi ^ 2} (M/N - 2{{(M/N)}^2})}}
\cdot {{\sin (2 \pi k M / N) } \over {k^2}}
\end{displaymath}">|; 

$key = q/d=pislashomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img706.png"
 ALT="$d=\pi/\omega$">|; 

$key = q/fbox{{mathrm{delwrite}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img820.png"
 ALT="\fbox{$\mathrm{delwrite}\sim$}">|; 

$key = q/0leqk<N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1045.png"
 ALT="$0 \leq k &lt; N$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="355" HEIGHT="244" BORDER="0"
 SRC="|."$dir".q|img1187.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.12.ps}\end{figure}">|; 

$key = q/{displaymath}cos(komega)approx1;,;sin(komega)approxkomega{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="187" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1308.png"
 ALT="\begin{displaymath}
\cos(k \omega) \approx 1 \; , \; \sin(k \omega) \approx k \omega
\end{displaymath}">|; 

$key = q/dslashR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img680.png"
 ALT="$d/R$">|; 

$key = q/z[0];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="$z[0]$">|; 

$key = q/{displaymath}P{x[n]+y[n]}=P{x[n]}+P{y[n]},hspace{0.1in}mathrm{whenever}{mathrm{COV}}{x[n],y[n]}=0{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="\begin{displaymath}
P \{x[n] + y[n]\} = P \{x[n]\} + P \{y[n]\} , \hspace{0.1in}
\mathrm{whenever}
 {\mathrm{COV}} \{ x[n] , y[n] \} = 0
\end{displaymath}">|; 

$key = q/{displaymath}f={{2^{hslash12}R}overN}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img197.png"
 ALT="\begin{displaymath}
f = {{2^{h/12} R} \over N}
\end{displaymath}">|; 

$key = q/pislash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$\pi /4$">|; 

$key = q/gle1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img774.png"
 ALT="$g \le 1$">|; 

$key = q/s=c=sqrt{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="100" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img761.png"
 ALT="$s = c = \sqrt{1/2}$">|; 

$key = q/{f_2}=1slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img516.png"
 ALT="${f_2}=1/2$">|; 

$key = q/{displaymath}x[n]=acos(alphan)+bcos(betan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="193" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img437.png"
 ALT="\begin{displaymath}
x[n] = a \cos(\alpha n) + b \cos(\beta n)
\end{displaymath}">|; 

$key = q/{displaymath}a[n]=mathrm{re}left[{{1over{1-{P}{Z^{-1}}}}{A{Z^n}+{1over{1-{P}{Z}}}overline{A}{Z^{-n}}}}right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img901.png"
 ALT="\begin{displaymath}
a[n] =
\mathrm{re} \left[ {
{1 \over {1 - {P}{Z^{-1}}}} {...
...n} +
{1 \over {1 - {P}{Z}}} \overline{A}{Z^{-n}}}
} \right ]
\end{displaymath}">|; 

$key = q/{displaymath}{(1-{r^2})-2ri}over{1+{r^2}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="95" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img934.png"
 ALT="\begin{displaymath}
{ (1 - {r^2}) - 2 r i }
\over
{ 1 + {r^2} }
\end{displaymath}">|; 

$key = q/y[1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="$y[1]$">|; 

$key = q/r=infty;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img930.png"
 ALT="$r=\infty$">|; 

$key = q/T'[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1196.png"
 ALT="$T'[k]$">|; 

$key = q/{figure}{psfig{file=figsslashfig02.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="175" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.01.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig10.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="464" BORDER="0"
 SRC="|."$dir".q|img1376.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.13.ps}\end{figure}">|; 

$key = q/1slashn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img309.png"
 ALT="$1/n$">|; 

$key = q/X''[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1273.png"
 ALT="$X''[n]$">|; 

$key = q/kge0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$k \ge 0$">|; 

$key = q/kcdotx[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$k \cdot x[n]$">|; 

$key = q/2M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1361.png"
 ALT="$2M$">|; 

$key = q/{displaymath}angle(Z)=mathrm{arctan}{left({bovera}right)}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img633.png"
 ALT="\begin{displaymath}
\angle(Z) = \mathrm{arctan}
{ \left ( {
b \over a
} \right ) }
\end{displaymath}">|; 

$key = q/1000;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img296.png"
 ALT="$1000$">|; 

$key = q/{displaymath}p[n]approx{1over{2{pi^2}}}left[{cos(omegan)}+{{cos(2omegan)}over4}+{{cos(3omegan)}over9}+cdotsright]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1333.png"
 ALT="\begin{displaymath}
p[n] \approx {1 \over {2 {\pi^2}}} \left [
{\cos ( \omega ...
...\over 4}
+ {{\cos ( 3 \omega n)} \over 9}
+ \cdots
\right ]
\end{displaymath}">|; 

$key = q/{displaymath}{Z^{-d}}=1{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="24" BORDER="0"
 SRC="|."$dir".q|img726.png"
 ALT="\begin{displaymath}
{Z^{-d}} = 1
\end{displaymath}">|; 

$key = q/{displaymath}N={{2^{hslash12}R}overf}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img198.png"
 ALT="\begin{displaymath}
N = {{2^{h/12} R} \over f}
\end{displaymath}">|; 

$key = q/{displaymath}f={{(t-1)R}overs}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img815.png"
 ALT="\begin{displaymath}
f = {{(t - 1) R} \over s}
\end{displaymath}">|; 

$key = q/0<a<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img510.png"
 ALT="$0&lt;a&lt;1$">|; 

$key = q/{displaymath}x[t]=cos(omega_cn)cos(acos(omega_mn))-sin(omega_cn)sin(acos(omega_mn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="403" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img535.png"
 ALT="\begin{displaymath}
x[t] = \cos( \omega_c n ) \cos (a \cos(\omega_m n))
- \sin( \omega_c n ) \sin (a \cos(\omega_m n))
\end{displaymath}">|; 

$key = q/fbox{{mathrm{select}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img342.png"
 ALT="\fbox{ $\mathrm{select}$ }">|; 

$key = q/{displaymath}={calFT}left{X[n]right}(k-{{alpha}over{omega}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="149" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1113.png"
 ALT="\begin{displaymath}
= {\cal FT} \left \{ X[n] \right \} (k - {{\alpha } \over {\omega}})
\end{displaymath}">|; 

$key = q/{displaymath}+A[N-1](cos(omega(N-1)n)+isin(omega(N-1)n)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1254.png"
 ALT="\begin{displaymath}
+ A[N-1](\cos(\omega (N-1) n) + i \sin(\omega (N-1) n))
\end{displaymath}">|; 

$key = q/{displaymath}{Z_1}{Z_2}={r_1}{r_2}cdotleft[cos({theta_1}+{theta_2})+isin({theta_1}+{theta_2})right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="294" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img647.png"
 ALT="\begin{displaymath}
{Z_1}{Z_2} = {r_1}{r_2}
\cdot \left[ \cos({\theta_1}+{\theta_2})
+ i \sin({\theta_1}+{\theta_2}) \right ]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.18.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="588" HEIGHT="252" BORDER="0"
 SRC="|."$dir".q|img937.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.18.ps}\end{figure}">|; 

$key = q/{displaymath}{y_1}[n]=c{x_1}[n]+s{x_2}[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img759.png"
 ALT="\begin{displaymath}
{y_1}[n] = c {x_1}[n] + s {x_2}[n]
\end{displaymath}">|; 

$key = q/C[m];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1158.png"
 ALT="$C[m]$">|; 

$key = q/2pislashd;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img704.png"
 ALT="$2\pi/d$">|; 

$key = q/{omega_c}slashomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img587.png"
 ALT="${\omega_c}/\omega$">|; 

$key = q/y[t];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img199.png"
 ALT="$y[t]$">|; 

$key = q/s[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1228.png"
 ALT="$s[k]$">|; 

$key = q/{displaymath}S[m,k];=;{{left|{{S[m-1,k]}over{T[k]}}right|}^{-1}};cdot;{{{S[m-1,k]T'[k]}over{T[k]}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="321" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img1194.png"
 ALT="\begin{displaymath}
S[m, k] \; = \;
{
{ \left \vert
{{S[m-1, k]}
\over
{...
...{-1}
}
\; \cdot \;
{
{{S[m-1, k] T'[k]}
\over
{T[k]}}
}
\end{displaymath}">|; 

$key = q/fbox{{mathrm{s}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="\fbox{ $\mathrm{s}$ }">|; 

$key = q/{d_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img807.png"
 ALT="${d_0}$">|; 

$key = q/omega=0,2pislashd,4pislashd,ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img727.png"
 ALT="$\omega = 0, 2\pi/d , 4\pi/d , \ldots$">|; 

$key = q/{displaymath}+{J_2}(a)cos((omega_c+2omega_m)n+pi)+{J_2}(a)cos((omega_c-2omega_m)n+pi){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="409" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img538.png"
 ALT="\begin{displaymath}
+ {J_2}(a) \cos( (\omega_c+2\omega_m) n + \pi)
+ {J_2}(a) \cos( (\omega_c-2\omega_m) n + \pi)
\end{displaymath}">|; 

$key = q/P=0.8;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$P=0.8$">|; 

$key = q/2omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="$2\omega $">|; 

$key = q/N-2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img261.png"
 ALT="$N-2$">|; 

$key = q/{displaymath}y[n]=n-d[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img788.png"
 ALT="\begin{displaymath}
y[n] = n - d[n]
\end{displaymath}">|; 

$key = q/J(Z)=H(R(S(Z)));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img964.png"
 ALT="$J(Z) = H(R(S(Z)))$">|; 

$key = q/{displaymath}{calFT}left{w[n]X[n]right}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1124.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ w[n] X[n] \right \} (k)
\end{displaymath}">|; 

$key = q/{displaymath}16{x^5}=cos(5omegan)+5cos(3omegan)+10cos(omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="296" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img497.png"
 ALT="\begin{displaymath}
16 {x^5} = \cos (5 \omega n) + 5 \cos(3 \omega n) + 10 \cos(\omega n)
\end{displaymath}">|; 

$key = q/{displaymath}Y[n]={Z^n}X[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1109.png"
 ALT="\begin{displaymath}
Y[n] = {Z^n} X[n]
\end{displaymath}">|; 

$key = q/{displaymath}f(-x)=-f(x){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img462.png"
 ALT="\begin{displaymath}
f(-x) = -f(x)
\end{displaymath}">|; 

$key = q/Nslash2M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1363.png"
 ALT="$N/2M$">|; 

$key = q/dslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$d/2$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="507" HEIGHT="499" BORDER="0"
 SRC="|."$dir".q|img470.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.08.ps}\end{figure}">|; 

$key = q/A,AZ,A{Z^2},ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img663.png"
 ALT="$A, AZ, A{Z^2}, \ldots$">|; 

$key = q/{displaymath}x[n]={d_1}s[n-{L_1}]+cdots+{d_j}s[n-{L_j}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="260" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img1289.png"
 ALT="\begin{displaymath}
x[n] = {d_1} s[n - {L_1}] + \cdots + {d_j} s[n - {L_j}]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig10.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="123" BORDER="0"
 SRC="|."$dir".q|img1342.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.07.ps}\end{figure}">|; 

$key = q/Rslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img300.png"
 ALT="$R/2$">|; 

$key = q/{figure}{psfig{file=figsslashfig03.16.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="496" HEIGHT="459" BORDER="0"
 SRC="|."$dir".q|img351.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.16.ps}\end{figure}">|; 

$key = q/{displaymath}X[n]={1overN}{calFT}left{Y[k]right}(-n){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1074.png"
 ALT="\begin{displaymath}
X[n] = {1 \over N} {\cal FT} \left \{ Y[k] \right \} (-n)
\end{displaymath}">|; 

$key = q/{displaymath}{Z^n}=cos(nomega)+isin(nomega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="173" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img655.png"
 ALT="\begin{displaymath}
{Z^n} = \cos(n\omega) + i \sin(n \omega)
\end{displaymath}">|; 

$key = q/{displaymath}m=ldots-2,-1,0,1,2,ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img480.png"
 ALT="\begin{displaymath}
m = \ldots -2, -1, 0, 1, 2, \ldots
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.22.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="343" BORDER="0"
 SRC="|."$dir".q|img814.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.22.ps}\end{figure}">|; 

$key = q/{displaymath}S(cos(omega)+isin(omega))=i{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img959.png"
 ALT="\begin{displaymath}
S(\cos(\omega) + i \sin(\omega)) = i
\end{displaymath}">|; 

$key = q/aslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img409.png"
 ALT="$a/2$">|; 

$key = q/{displaymath}{fbox{texttt{delread~}}{longrightarrowx[N],ldots,x[N+B-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img829.png"
 ALT="\begin{displaymath}
\fbox{\texttt{delread\&nbsp;}} \longrightarrow x[N], \ldots, x[N+B-1]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig06.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="361" HEIGHT="373" BORDER="0"
 SRC="|."$dir".q|img615.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.15.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="468" BORDER="0"
 SRC="|."$dir".q|img279.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.14.ps}\end{figure}">|; 

$key = q/0len<N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1312.png"
 ALT="$0 \le n &lt; N$">|; 

$key = q/a=mathop{mathgroupsymoperatorscos}nolimits(theta)=mathop{mathgroupsymoperatorssin}nolimits(theta)=sqrt{1slash2}approx0.7071;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="$a = \mathop {\mathgroup \symoperators cos}\nolimits (\theta ) = \mathop {\mathgroup \symoperators sin}\nolimits (\theta ) = \sqrt {1/2} \approx 0.7071$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.27.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="388" HEIGHT="328" BORDER="0"
 SRC="|."$dir".q|img997.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.27.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{stripnote}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img353.png"
 ALT="\fbox{ $\mathrm{stripnote}$}">|; 

$key = q/{figure}{psfig{file=figsslashfig10.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="479" HEIGHT="293" BORDER="0"
 SRC="|."$dir".q|img1282.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.03.ps}\end{figure}">|; 

$key = q/{displaymath}omega_c+3omega_m+komega_p,k=0,pm1,pm2,ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img546.png"
 ALT="\begin{displaymath}
\omega_c+3\omega_m + k \omega_p , k = 0, \pm 1, \pm 2, \ldots
\end{displaymath}">|; 

$key = q/{displaymath}{a_0}={a_0}cos(0cdotomegan),{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img404.png"
 ALT="\begin{displaymath}
{a_0} = {a_0}\cos(0 \cdot \omega n),
\end{displaymath}">|; 

$key = q/omega=alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img869.png"
 ALT="$\omega = \alpha$">|; 

$key = q/@mathrm{fft}sim;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="$\@mathrm {fft}\sim $">|; 

$key = q/{figure}{psfig{file=figsslashfig03.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="346" HEIGHT="160" BORDER="0"
 SRC="|."$dir".q|img330.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.06.ps}\end{figure}">|; 

$key = q/{displaymath}cos(a)cos(b)={1over2}{left[{parbox[t][0.1in]{0in}{mbox{}}{cos(a+b)+cos(a-b)right]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="287" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img411.png"
 ALT="\begin{displaymath}
\cos(a) \cos (b) = {1 \over 2}
{ \left [
\parbox[t][0.1in]{0in}{\mbox{}}
\cos (a+b) + \cos(a-b)
\right ] }
\end{displaymath}">|; 

$key = q/{displaymath}f(x)=cos(x)cos(phi)-sin(x)sin(phi){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img531.png"
 ALT="\begin{displaymath}
f(x) = \cos(x) \cos(\phi) - \sin(x) \sin(\phi)
\end{displaymath}">|; 

$key = q/T'[k+1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1197.png"
 ALT="$T'[k+1]$">|; 

$key = q/V={U^{-k}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1058.png"
 ALT="$V = {U^{-k}}$">|; 

$key = q/{sqrt2}a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="${\sqrt 2} a$">|; 

$key = q/{displaymath}f(x)=cos(x+phi){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="122" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img526.png"
 ALT="\begin{displaymath}
f(x) = \cos(x + \phi)
\end{displaymath}">|; 

$key = q/{theta_1}+{theta_2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img650.png"
 ALT="${\theta_1}+{\theta_2}$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.19.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="467" HEIGHT="247" BORDER="0"
 SRC="|."$dir".q|img951.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.19.ps}\end{figure}">|; 

$key = q/a=b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$a=b$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="470" HEIGHT="265" BORDER="0"
 SRC="|."$dir".q|img1099.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.01.ps}\end{figure}">|; 

$key = q/|X|=|Y|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img758.png"
 ALT="$\vert X\vert = \vert Y\vert$">|; 

$key = q/{displaymath}s[n]-s[n-1]=-{1overN}+left{array{{ll}{1}&{n=0}0&mbox{otherwise}array{right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1313.png"
 ALT="\begin{displaymath}
s[n] - s[n-1] = -{1 \over N} +
\left \{
\begin{array}{ll}
{1} &amp; {n = 0} \\\\
0 &amp; \mbox{otherwise}
\end{array} \right .
\end{displaymath}">|; 

$key = q/f(x)=x^k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="35" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img504.png"
 ALT="$f(x) = x^k$">|; 

$key = q/k=0,ldots,N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1076.png"
 ALT="$k=0,
\ldots, N-1$">|; 

$key = q/angle(ZW);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1000.png"
 ALT="$\angle(ZW)$">|; 

$key = q/{displaymath}approx-s[n]slashN.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1329.png"
 ALT="\begin{displaymath}
\approx - s[n] / N .
\end{displaymath}">|; 

$key = q/fbox{texttt{vcf~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1022.png"
 ALT="\fbox{ \texttt{vcf\&nbsp;}}">|; 

$key = q/{displaymath}A{Z^n}+overline{A}{Z^{-n}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="25" BORDER="0"
 SRC="|."$dir".q|img900.png"
 ALT="\begin{displaymath}
A{Z^n} + \overline{A}{Z^{-n}}
\end{displaymath}">|; 

$key = q/X[N-n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1268.png"
 ALT="$X[N-n]$">|; 

$key = q/2n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img963.png"
 ALT="$2n$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="421" HEIGHT="466" BORDER="0"
 SRC="|."$dir".q|img525.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.13.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.18.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="447" HEIGHT="172" BORDER="0"
 SRC="|."$dir".q|img798.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.18.ps}\end{figure}">|; 

$key = q/fbox{texttt{q8_rsqrt~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1243.png"
 ALT="\fbox{\texttt{q8\_rsqrt\&nbsp;}}">|; 

$key = q/{displaymath}V=cos(-komega)+isin(-komega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="188" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1060.png"
 ALT="\begin{displaymath}
V = \cos(-k\omega) + i\sin(-k\omega)
\end{displaymath}">|; 

$key = q/{displaymath}={V^{0}}X[-d]+{V^{1}}X[-d+1]+cdots+{V^{N-1}}X[-d+N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="393" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1102.png"
 ALT="\begin{displaymath}
=
{V ^ {0}} X[-d] +
{V ^ {1}} X[-d+1] +
\cdots +
{V ^ {N-1}} X[-d+N-1]
\end{displaymath}">|; 

$key = q/X[n]=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1077.png"
 ALT="$X[n]=1$">|; 

$key = q/X[-m];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1070.png"
 ALT="$X[-m]$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="121" BORDER="0"
 SRC="|."$dir".q|img416.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.02.ps}\end{figure}">|; 

$key = q/s'[n]=ds[n-L];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1288.png"
 ALT="$s'[n] = d s[n-L]$">|; 

$key = q/omega_c;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img464.png"
 ALT="$\omega_c$">|; 

$key = q/fbox{{mathrm{expr}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img287.png"
 ALT="\fbox{ $\mathrm{expr}$ }">|; 

$key = q/{figure}{psfig{file=figsslashfig08.28.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="190" BORDER="0"
 SRC="|."$dir".q|img1021.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.28.ps}\end{figure}">|; 

$key = q/{displaymath}{AZ^n}=acdot[cos(nomega+phi)+isin(nomega+phi)]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="272" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img661.png"
 ALT="\begin{displaymath}
{AZ^n} = a \cdot [\cos(n \omega + \phi) + i \sin(n \omega + \phi)]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.17.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="291" BORDER="0"
 SRC="|."$dir".q|img936.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.17.ps}\end{figure}">|; 

$key = q/H_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1007.png"
 ALT="$H_2$">|; 

$key = q/{displaymath}{P_1}=pcdot(cosomega+isinomega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img925.png"
 ALT="\begin{displaymath}
{P_1} = p \cdot (\cos \omega + i \sin \omega)
\end{displaymath}">|; 

$key = q/n-d[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img786.png"
 ALT="$n - d[n]$">|; 

$key = q/N+2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img268.png"
 ALT="$N+2$">|; 

$key = q/{displaymath}f(acdotx[n])={f_0}+a{f_1}cos(omegan)+{a^2}{f_2}{cos^2}(omegan)+{a^3}{f_3}{cos^3}(omegan)+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="461" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img451.png"
 ALT="\begin{displaymath}
f(a \cdot x[n]) = {f_0} + a {f_1}\cos(\omega n) + {a^2} {f_...
...\cos^2} (\omega n)
+ {a^3} {f_3} {\cos^3} (\omega n) + \cdots
\end{displaymath}">|; 

$key = q/T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img557.png"
 ALT="$T$">|; 

$key = q/{displaymath}{H_1}(Z)approx-i{H_2}(Z),;-pi<angle(Z)<0{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1010.png"
 ALT="\begin{displaymath}
{H_1}(Z) \approx -i {H_2}(Z) , \; -\pi &lt; \angle(Z) &lt; 0
\end{displaymath}">|; 

$key = q/{displaymath}{calFT}left{X[n-d]right}(k)=left({{parbox[t][0.1in]{0in}{mbox{}}{codkomega)+isin(-dkomega)}right){calFT}left{X[n]right}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="447" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1106.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ X[n-d] \right \} (k) =
\left ( {
\par...
...-dk\omega)
} \right )
{\cal FT} \left \{ X[n] \right \} (k)
\end{displaymath}">|; 

$key = q/fbox{{mathrm{env}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img349.png"
 ALT="\fbox{ $\mathrm{env}\sim$}">|; 

$key = q/k=pm1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1320.png"
 ALT="$k = \pm 1$">|; 

$key = q/{displaymath}+A[N-1](cos(omega(N-1)n)-isin(omega(N-1)n)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1270.png"
 ALT="\begin{displaymath}
+ A[N-1](\cos(\omega (N-1) n) - i \sin(\omega (N-1) n))
\end{displaymath}">|; 

$key = q/fbox{{mathrm{throwsim}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img389.png"
 ALT="\fbox{$\mathrm{throw\sim}$}">|; 

$key = q/2<a<3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img512.png"
 ALT="$2&lt;a&lt;3$">|; 

$key = q/{displaymath}{a_1}=y[{x_0}+1]-y[{x_0}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img251.png"
 ALT="\begin{displaymath}
{a_1} = y[{x_0} + 1]- y[{x_0}]
\end{displaymath}">|; 

$key = q/{displaymath}=angleleft({{S[m-1,k]T'[k]}over{T[k]}}right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1191.png"
 ALT="\begin{displaymath}
= \angle \left (
{{S[m-1, k] T'[k]}
\over
{T[k]}}
\right )
\end{displaymath}">|; 

$key = q/2pislash10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$2\pi /10$">|; 

$key = q/{figure}{psfig{file=figsslashfig03.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="585" HEIGHT="515" BORDER="0"
 SRC="|."$dir".q|img333.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.08.ps}\end{figure}">|; 

$key = q/{displaymath}+ableft[cos((alpha+beta)n)+cos((alpha-beta)n)right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="247" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img440.png"
 ALT="\begin{displaymath}
+ a b \left [
\cos ( (\alpha + \beta) n ) + \cos ( (\alpha - \beta) n )
\right ]
\end{displaymath}">|; 

$key = q/{displaymath}X[n]=Z^n{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img710.png"
 ALT="\begin{displaymath}
X[n] = Z^n
\end{displaymath}">|; 

$key = q/{displaymath}X[n]=A{Z^n},Y[n]=B{Z^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img665.png"
 ALT="\begin{displaymath}
X[n] = A {Z^n} ,  Y[n] = B {Z^n}
\end{displaymath}">|; 

$key = q/({x_1},{x_2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img753.png"
 ALT="$({x_1}, {x_2})$">|; 

$key = q/fbox{texttt{bang~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1231.png"
 ALT="\fbox{\texttt{bang\&nbsp;}}">|; 

$key = q/{displaymath}x[t]=cos(omega_cn+acos(omega_mn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="198" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img533.png"
 ALT="\begin{displaymath}
x[t] = \cos( \omega_c n + a \cos(\omega_m n))
\end{displaymath}">|; 

$key = q/aslash{sqrt2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$a / {\sqrt 2}$">|; 

$key = q/Z;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$Z$">|; 

$key = q/{displaymath}x[n]=c(omegan){m_a}(omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img559.png"
 ALT="\begin{displaymath}
x[n] = c(\omega n) {m_a}(\omega n)
\end{displaymath}">|; 

$key = q/S[m,k+1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1195.png"
 ALT="$S[m,k+1]$">|; 

$key = q/{displaymath}x[n]approx{1overpi}left[{sin(omegan)}+{{sin(2omegan)}over2}+{{sin(3omegan)}over3}+cdotsright.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1337.png"
 ALT="\begin{displaymath}
x[n] \approx {1 \over \pi} \left [
{\sin ( \omega n )}
+ ...
...\over 2}
+ {{\sin ( 3 \omega n)} \over 3}
+ \cdots
\right .
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig01.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="555" HEIGHT="350" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.12.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="334" BORDER="0"
 SRC="|."$dir".q|img368.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.05.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="453" HEIGHT="278" BORDER="0"
 SRC="|."$dir".q|img218.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.06.ps}\end{figure}">|; 

$key = q/X[-n]=-X[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1276.png"
 ALT="$X[-n] = -X[n]$">|; 

$key = q/f(x)=sin(x);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img474.png"
 ALT="$f(x) = \sin(x)$">|; 

$key = q/S[m,k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$S[m, k]$">|; 

$key = q/{displaymath}f(x[n])={{a^2}over2}left(1+cos(2omegan+2phi)right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="229" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img435.png"
 ALT="\begin{displaymath}
f(x[n]) = {{a^2} \over 2} \left ( 1 + \cos(2 \omega n + 2 \phi) \right )
\end{displaymath}">|; 

$key = q/{displaymath}{2over{5pi}}-{1over2}[{2over{3pi}}+{2over{7pi}}]approx-32.30mathrm{dB}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1139.png"
 ALT="\begin{displaymath}
{2 \over {5 \pi}} - {1\over 2} [ {2 \over {3 \pi}} + {2 \over {7 \pi}} ]
\approx -32.30 \mathrm{dB}
\end{displaymath}">|; 

$key = q/k=3slash2,5slash2,ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1137.png"
 ALT="$k = 3/2, 5/2, \ldots$">|; 

$key = q/{displaymath}f=440cdot{{2}^{(m-69)slash12}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="\begin{displaymath}
f = 440 \cdot {{2} ^ {(m - 69) / 12}}
\end{displaymath}">|; 

$key = q/{displaymath}{{left(1-{1overn}right)}^n}approx{1overe}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img976.png"
 ALT="\begin{displaymath}
{ {\left ( 1-{1\over n} \right ) } ^ n } \approx {1\over e}
\end{displaymath}">|; 

$key = q/{displaymath}t=1-{{sf}overR}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img813.png"
 ALT="\begin{displaymath}
t = 1 - {{sf} \over R}
\end{displaymath}">|; 

$key = q/Z^-d;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="$Z^-d$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.26.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="238" BORDER="0"
 SRC="|."$dir".q|img990.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.26.ps}\end{figure}">|; 

$key = q/theta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img634.png"
 ALT="$\theta$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.16.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="536" HEIGHT="245" BORDER="0"
 SRC="|."$dir".q|img927.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.16.ps}\end{figure}">|; 

$key = q/pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$\pi /2$">|; 

$key = q/Y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img672.png"
 ALT="$Y$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="312" HEIGHT="211" BORDER="0"
 SRC="|."$dir".q|img858.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.05.ps}\end{figure}">|; 

$key = q/{displaymath}x[n]=acdotcos(alphan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img991.png"
 ALT="\begin{displaymath}
x[n] = a \cdot \cos(\alpha n)
\end{displaymath}">|; 

$key = q/H_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1006.png"
 ALT="$H_1$">|; 

$key = q/({L_2},{d_2})=(0.6N,1.3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1284.png"
 ALT="$({L_2}, {d_2}) = (0.6N, 1.3)$">|; 

$key = q/{Z^{-d}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img676.png"
 ALT="${Z^{-d}}$">|; 

$key = q/R'[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1245.png"
 ALT="$R'[k]$">|; 

$key = q/{displaymath}alpha={{angleS[1,3]-angleS[0,3]+2ppi}overH}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1182.png"
 ALT="\begin{displaymath}
\alpha = {{\angle S[1, 3] - \angle S[0, 3] + 2 p \pi} \over H}
\end{displaymath}">|; 

$key = q/{displaymath}{calFT}left{X[n]right}(k)={V^{0}}X[0]+{V^{1}}X[1]+cdots+{V^{N-1}}X[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="406" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1057.png"
 ALT="\begin{displaymath}
{\cal FT}\left \{ X[n] \right \} (k) =
{V ^ {0}} X[0] +
{V ^ {1}} X[1] +
\cdots +
{V ^ {N-1}} X[N-1]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig01.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="266" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.05.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig03.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="533" HEIGHT="279" BORDER="0"
 SRC="|."$dir".q|img310.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.02.ps}\end{figure}">|; 

$key = q/{displaymath}sin(acos(omega_mn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="107" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img476.png"
 ALT="\begin{displaymath}
\sin(a \cos(\omega_m n))
\end{displaymath}">|; 

$key = q/1slasha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img580.png"
 ALT="$1/a$">|; 

$key = q/X[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img669.png"
 ALT="$X[n]$">|; 

$key = q/eapprox2.7;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img520.png"
 ALT="$e \approx 2.7$">|; 

$key = q/R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="$R$">|; 

$key = q/{a^2}{f_2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img509.png"
 ALT="${a^2}{f_2}$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="447" HEIGHT="623" BORDER="0"
 SRC="|."$dir".q|img1176.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.10.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.33.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="443" HEIGHT="518" BORDER="0"
 SRC="|."$dir".q|img849.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.33.ps}\end{figure}">|; 

$key = q/{displaymath}=mathrm{re}left[{{{1-mathrm{re}(P){Z^{-1}}}over{(1-{P}{Z^{-1}})(1-{ne{Z}}^{-1}})}}{overline{A}{{overline{Z}}^{-n}}}}right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img904.png"
 ALT="\begin{displaymath}
=
\mathrm{re} \left[ {
{{
1 - \mathrm{re} (P) {Z^{-1}}
...
...}}^{-1}})
}}
{\overline{A}{{\overline{Z}}^{-n}}}
} \right ]
\end{displaymath}">|; 

$key = q/1,1slash2,1slash3,ldots,1slashb;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1235.png"
 ALT="$1, 1/2, 1/3, \ldots, 1/b$">|; 

$key = q/{displaymath}=cos((omega-pi)n+phi){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img303.png"
 ALT="\begin{displaymath}
= \cos((\omega - \pi)n + \phi)
\end{displaymath}">|; 

$key = q/f,3f,ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img843.png"
 ALT="$f, 3f, \ldots$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.18.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="589" HEIGHT="851" BORDER="0"
 SRC="|."$dir".q|img1240.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.18.ps}\end{figure}">|; 

$key = q/{displaymath}16{x^5}-20{x^3}+5x=cos(5omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img500.png"
 ALT="\begin{displaymath}
16 {x^5} - 20 {x^3} + 5 x = \cos (5 \omega n)
\end{displaymath}">|; 

$key = q/{displaymath}x[n]=acdotcos(alphan)+bcdotcos(betan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="211" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img995.png"
 ALT="\begin{displaymath}
x[n] = a \cdot \cos(\alpha n) + b \cdot \cos(\beta n)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig03.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="574" HEIGHT="534" BORDER="0"
 SRC="|."$dir".q|img321.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.04.ps}\end{figure}">|; 

$key = q/{displaymath}+{b_0}+{b_1}cosleft(omegan+pi+{theta_1}right)+{b_2}cosleft(2omegan+2pi+{theta_2}right)+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="389" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img230.png"
 ALT="\begin{displaymath}
+
{b_0} +
{b_1} \cos \left ( \omega n + \pi + {\theta_1} ...
...\cos \left ( 2 \omega n + 2 \pi + {\theta_2} \right ) + \cdots
\end{displaymath}">|; 

$key = q/x[n]=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$x[n] = 1$">|; 

$key = q/sqrt{1slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="38" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img847.png"
 ALT="$\sqrt{1/2}$">|; 

$key = q/omega=2pislashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1047.png"
 ALT="$\omega=2\pi/N$">|; 

$key = q/{figure}{psfig{file=figsslashfig03.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="413" HEIGHT="551" BORDER="0"
 SRC="|."$dir".q|img331.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.07.ps}\end{figure}">|; 

$key = q/R';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1210.png"
 ALT="$R'$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="482" HEIGHT="245" BORDER="0"
 SRC="|."$dir".q|img1144.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.06.ps}\end{figure}">|; 

$key = q/c(phi)=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img595.png"
 ALT="$c(\phi) = 1$">|; 

$key = q/|S[m,k]|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1173.png"
 ALT="$\vert S[m, k]\vert$">|; 

$key = q/(Nslash2,-8);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="$(N/2, -8)$">|; 

$key = q/af_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img508.png"
 ALT="$af_1$">|; 

$key = q/{displaymath}{(1-{r^2})-(2rsin(alpha))i}over{1+{r^2}+2rcos(alpha))}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img931.png"
 ALT="\begin{displaymath}
{ (1 - {r^2}) - (2 r \sin(\alpha)) i }
\over
{ 1 + {r^2} + 2 r \cos(\alpha))}
\end{displaymath}">|; 

$key = q/{displaymath}x[t+tauslash3]=x[t]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img444.png"
 ALT="\begin{displaymath}
x[t + \tau/3] = x[t]
\end{displaymath}">|; 

$key = q/{displaymath}d[n]={d_0}+acos(omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img800.png"
 ALT="\begin{displaymath}
d[n] = {d_0} + a \cos(\omega n)
\end{displaymath}">|; 

$key = q/m=0,ldots,N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1069.png"
 ALT="$m = 0, \ldots, N-1$">|; 

$key = q/n=-m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1073.png"
 ALT="$n = -m$">|; 

$key = q/cos(-domega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="68" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img689.png"
 ALT="$\cos(-d \omega)$">|; 

$key = q/{displaymath}g[m,k]=left{array{{ll}{1-f[k]slash|S[m,k]|}&{|S[m,k]|>f[k]}0&mbox{otherwise}array{right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="330" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1166.png"
 ALT="\begin{displaymath}
g[m, k] =
\left \{
\begin{array}{ll}
{1 - f[k]/\vert S[...
...]\vert &gt; f[k]} \\\\
0 &amp; \mbox{otherwise}
\end{array} \right .
\end{displaymath}">|; 

$key = q/omega=pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img797.png"
 ALT="$\omega = \pi / 2$">|; 

$key = q/{displaymath}x[n]=s[n]-s[n-{Nover2}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="155" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1335.png"
 ALT="\begin{displaymath}
x[n] = s[n] - s[n-{N \over 2}]
\end{displaymath}">|; 

$key = q/c[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1237.png"
 ALT="$c[k]$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="583" HEIGHT="428" BORDER="0"
 SRC="|."$dir".q|img381.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.14.ps}\end{figure}">|; 

$key = q/overline{W};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img957.png"
 ALT="$\overline{W}$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="403" BORDER="0"
 SRC="|."$dir".q|img579.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.04.ps}\end{figure}">|; 

$key = q/omega=arg(Z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img861.png"
 ALT="$\omega=\arg(Z)$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.16.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="441" HEIGHT="438" BORDER="0"
 SRC="|."$dir".q|img540.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.16.ps}\end{figure}">|; 

$key = q/0,1,...B-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img313.png"
 ALT="$0, 1, ... B-1$">|; 

$key = q/0lef<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img324.png"
 ALT="$0 \le f &lt; 1$">|; 

$key = q/{displaymath}{calFT}{s[n]-s[n-1]}(k)=1,;kneq0,;-N<k<N{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="344" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1315.png"
 ALT="\begin{displaymath}
{\cal FT}\{ s[n] - s[n-1] \} (k) = 1 , \; k \neq 0, \; -N &lt; k &lt; N\
\end{displaymath}">|; 

$key = q/{2^m}+3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img274.png"
 ALT="${2^m} + 3$">|; 

$key = q/{displaymath}{y_{mathrm{INT}}}(x)={displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img254.png"
 ALT="\begin{displaymath}
{y_{\mathrm{INT}}}(x) =
\end{displaymath}">|; 

$key = q/{D_N};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1118.png"
 ALT="${D_N}$">|; 

$key = q/{x_0};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img244.png"
 ALT="${x_0}$">|; 

$key = q/{displaymath}{a_0}=2{b_0},,,{a_1}=2{b_2},,,{a_2}=2{b_4}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img232.png"
 ALT="\begin{displaymath}
{a_0} = 2{b_0},    {a_1} = 2{b_2},    {a_2} = 2{b_4}
\end{displaymath}">|; 

$key = q/(0,8);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="$(0, 8)$">|; 

$key = q/beta=pislash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="$\beta = \pi /4$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.32.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="230" HEIGHT="164" BORDER="0"
 SRC="|."$dir".q|img848.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.32.ps}\end{figure}">|; 

$key = q/D_N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$D_N$">|; 

$key = q/{displaymath}x[1.5]={{-x[0]+9x[1]+9x[2]-x[3]}over8}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="250" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img792.png"
 ALT="\begin{displaymath}
x[1.5] = {{-x[0] + 9x[1] + 9 x[2] - x[3]} \over 8}
\end{displaymath}">|; 

$key = q/N>1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1078.png"
 ALT="$N&gt;1$">|; 

$key = q/fbox{{mathrm{rzero_rev}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1032.png"
 ALT="\fbox{$\mathrm{rzero\_rev}\sim$}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.19.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="380" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img799.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.19.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.20.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="545" HEIGHT="244" BORDER="0"
 SRC="|."$dir".q|img972.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.20.ps}\end{figure}">|; 

$key = q/-49;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1141.png"
 ALT="$-49$">|; 

$key = q/{displaymath}{calFT}left{Y[n]right}(k)={V^{0}}Y[0]+{V^{1}}Y[1]+cdots+{V^{N-1}}Y[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="400" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1101.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ Y[n] \right \} (k) =
{V ^ {0}} Y[0] +
{V ^ {1}} Y[1] +
\cdots +
{V ^ {N-1}} Y[N-1]
\end{displaymath}">|; 

$key = q/a=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$a=1$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="369" BORDER="0"
 SRC="|."$dir".q|img382.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.15.ps}\end{figure}">|; 

$key = q/{r_1}{r_2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img649.png"
 ALT="${r_1}{r_2}$">|; 

$key = q/komega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1145.png"
 ALT="$k\omega$">|; 

$key = q/{displaymath}f(x)={f_0}+{f_1}x+{f_2}{x^2}+cdots,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img505.png"
 ALT="\begin{displaymath}
f(x) = {f_0} + {f_1} x + {f_2} {x^2} + \cdots,
\end{displaymath}">|; 

$key = q/U;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1048.png"
 ALT="$U$">|; 

$key = q/2f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img844.png"
 ALT="$2f$">|; 

$key = q/sin(theta)approxtheta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1358.png"
 ALT="$\sin(\theta) \approx \theta$">|; 

$key = q/cosomega+isinomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img920.png"
 ALT="$\cos \omega + i \sin \omega$">|; 

$key = q/1+b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img606.png"
 ALT="$1+b$">|; 

$key = q/{figure}{psfig{file=figsslashfig03.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="463" HEIGHT="692" BORDER="0"
 SRC="|."$dir".q|img350.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.15.ps}\end{figure}">|; 

$key = q/{displaymath}Y[n]=(1+g{Z^{-d}}+{g^2}{Z^{-2d}}+cdots)X[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="270" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img711.png"
 ALT="\begin{displaymath}
Y[n] = (1 + g{Z^{-d}} + {g^2}{Z^{-2d}} + \cdots) X[n]
\end{displaymath}">|; 

$key = q/omega,2omega,ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$\omega, 2 \omega, \ldots$">|; 

$key = q/-omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1004.png"
 ALT="$-\omega$">|; 

$key = q/nomega+phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img660.png"
 ALT="$n \omega + \phi$">|; 

$key = q/{displaymath}T[k]={calFT}(W(n)X[n])(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1188.png"
 ALT="\begin{displaymath}
T[k] = {\cal FT}(W(n)X[n]) (k)
\end{displaymath}">|; 

$key = q/k=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1098.png"
 ALT="$k=-1$">|; 

$key = q/Y={y_1}+{y_2}i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img756.png"
 ALT="$Y={y_1} + {y_2}i$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="251" HEIGHT="382" BORDER="0"
 SRC="|."$dir".q|img554.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.02.ps}\end{figure}">|; 

$key = q/{displaymath}{{1-{r^2}}over{{(1+r)}^2}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="48" BORDER="0"
 SRC="|."$dir".q|img928.png"
 ALT="\begin{displaymath}
{{1 - {r^2}} \over {{(1 + r)}^2}}
\end{displaymath}">|; 

$key = q/x_{200};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img235.png"
 ALT="$x_{200}$">|; 

$key = q/{displaymath}overline{A}=a-bi=rcdot(cos(alpha)-isin(alpha)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img874.png"
 ALT="\begin{displaymath}
\overline{A} = a-bi = r \cdot (\cos(\alpha) - i \sin(\alpha))
\end{displaymath}">|; 

$key = q/{displaymath}{2over{3pi}}approx-13mathrm{dB},;{2over{5pi}}approx-18mathrm{dB},;{rox-21mathrm{dB},;{2over{9pi}}approx-23mathrm{dB},ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="420" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1138.png"
 ALT="\begin{displaymath}
{2 \over {3 \pi}} \approx -13 \mathrm{dB} , \;
{2 \over {5...
...{dB} , \;
{2 \over {9 \pi}} \approx -23 \mathrm{dB} ,
\ldots
\end{displaymath}">|; 

$key = q/fbox{{mathrm{vd}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img826.png"
 ALT="\fbox{$\mathrm{vd}\sim$}">|; 

$key = q/x[n-d];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="58" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img781.png"
 ALT="$x[n-d]$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.30.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="524" HEIGHT="435" BORDER="0"
 SRC="|."$dir".q|img1025.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.30.ps}\end{figure}">|; 

$key = q/fbox{texttt{rzero~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1028.png"
 ALT="\fbox{ \texttt{rzero\&nbsp;}}">|; 

$key = q/{figure}{psfig{file=figsslashfig03.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="311" HEIGHT="110" BORDER="0"
 SRC="|."$dir".q|img306.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.01.ps}\end{figure}">|; 

$key = q/angle(Z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img632.png"
 ALT="$\angle(Z)$">|; 

$key = q/fbox{{mathrm{fft}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1217.png"
 ALT="\fbox{$\mathrm{fft}\sim$}">|; 

$key = q/{xi^2}=V;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1083.png"
 ALT="${\xi^2} = V$">|; 

$key = q/{x_{50}}[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img224.png"
 ALT="${x_{50}}[n]$">|; 

$key = q/{Z^{dslash2}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img691.png"
 ALT="${Z^{d/2}}$">|; 

$key = q/W(phi)=(1+cos(phi))slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img578.png"
 ALT="$W(\phi)=(1+\cos(\phi))/2$">|; 

$key = q/0.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img613.png"
 ALT="$0.5$">|; 

$key = q/{displaymath}h(x)={1over{1+{x^2}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img569.png"
 ALT="\begin{displaymath}
h(x) = {1\over{1 + {x^2}}}
\end{displaymath}">|; 

$key = q/omega_m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img463.png"
 ALT="$\omega_m$">|; 

$key = q/j=k=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img771.png"
 ALT="$j=k=1$">|; 

$key = q/{displaymath}cos(omega_cn+acos(omega_mn+bcos(omega_pn))){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="243" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img550.png"
 ALT="\begin{displaymath}
\cos( \omega_c n + a \cos( \omega_m n + b \cos( \omega_p n )))
\end{displaymath}">|; 

$key = q/{displaymath}f(x)=16{x^5}-20{x^3}+5x{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="170" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img501.png"
 ALT="\begin{displaymath}
f(x) = 16 {x^5} - 20 {x^3} + 5 x
\end{displaymath}">|; 

$key = q/{Q_1},ldots,{Q_j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img887.png"
 ALT="${Q_1}, \ldots, {Q_j}$">|; 

$key = q/{displaymath}H(Z)=(1-{Q}{Z^{-1}})cdot(1-overline{Q}{Z^{-1}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img891.png"
 ALT="\begin{displaymath}
H(Z) = (1 - {Q}{Z^{-1}}) \cdot (1 - \overline{Q}{Z^{-1}})
\end{displaymath}">|; 

$key = q/{displaymath}{left.{+ileft(sin({theta_1})cos({theta_2})+cos({theta_1})sin({theta_2})right)}right]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="249" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img644.png"
 ALT="\begin{displaymath}
{ \left . {
+ i \left (
\sin({\theta_1}) \cos({\theta_2}) +
\cos({\theta_1}) \sin({\theta_2})
\right )
} \right ] }
\end{displaymath}">|; 

$key = q/x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img243.png"
 ALT="$x$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="394" HEIGHT="276" BORDER="0"
 SRC="|."$dir".q|img490.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.11.ps}\end{figure}">|; 

$key = q/{displaymath}cos(pik(N-1)slashN)-isin(pik(N-1)slashN){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="280" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1094.png"
 ALT="\begin{displaymath}
\cos(\pi k (N-1)/N) - i \sin(\pi k (N-1)/N)
\end{displaymath}">|; 

$key = q/fbox{{mathrm{pack}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img278.png"
 ALT="\fbox{ $\mathrm{pack}$ }">|; 

$key = q/{displaymath}16{x^5}-20{x^3}=cos(5omegan)-5cos(omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="248" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img499.png"
 ALT="\begin{displaymath}
16 {x^5} - 20 {x^3} = \cos (5 \omega n) - 5 \cos(\omega n)
\end{displaymath}">|; 

$key = q/j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img769.png"
 ALT="$j$">|; 

$key = q/{displaymath}{x_{200}}[2n]={x_{100}}[n]+{x_{100}}[n+{pioveromega}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img236.png"
 ALT="\begin{displaymath}
{x_{200}}[2n] = {x_{100}}[n] + {x_{100}}[n+{\pi \over \omega}]
\end{displaymath}">|; 

$key = q/P{x[n]};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$P\{x[n]\}$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="349" HEIGHT="429" BORDER="0"
 SRC="|."$dir".q|img611.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.13.ps}\end{figure}">|; 

$key = q/{displaymath}X[n]=aleft(cos(omegan)+isin(omegan)right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="210" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1002.png"
 ALT="\begin{displaymath}
X[n] = a \left ( \cos (\omega n) + i \sin (\omega n) \right )
\end{displaymath}">|; 

$key = q/{displaymath}{a_0}=y[{x_0}]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img250.png"
 ALT="\begin{displaymath}
{a_0} = y[{x_0}]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="298" HEIGHT="296" BORDER="0"
 SRC="|."$dir".q|img764.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.13.ps}\end{figure}">|; 

$key = q/{displaymath}x[n+tau]=x[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="\begin{displaymath}
x[n + \tau] = x[n]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig01.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="362" HEIGHT="306" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.02.ps}\end{figure}">|; 

$key = q/alpha-beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img415.png"
 ALT="$\alpha-\beta$">|; 

$key = q/{displaymath}alpha_1+beta,alpha_1-beta,ldots,alpha_k+beta,alpha_k-beta{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="236" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img429.png"
 ALT="\begin{displaymath}
\alpha_1 + \beta, \alpha_1 - \beta, \ldots,
\alpha_k + \beta, \alpha_k - \beta
\end{displaymath}">|; 

$key = q/SslashT;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1203.png"
 ALT="$S/T$">|; 

$key = q/l-sslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img215.png"
 ALT="$l-s/2$">|; 

$key = q/k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$k$">|; 

$key = q/{displaymath}k<{{1}over{4MslashN}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1357.png"
 ALT="\begin{displaymath}
k &lt; {{1} \over {4 M/N}}
\end{displaymath}">|; 

$key = q/8pislashN=4omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1184.png"
 ALT="$8\pi/N = 4 \omega$">|; 

$key = q/{displaymath}{Z_1}={r_1}cdotleft[cos({theta_1})+isin({theta_1})right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img641.png"
 ALT="\begin{displaymath}
{Z_1} = {r_1} \cdot \left [ \cos({\theta_1}) + i \sin({\theta_1}) \right ]
\end{displaymath}">|; 

$key = q/phi=-pislash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img527.png"
 ALT="$\phi=-\pi/2$">|; 

$key = q/W^n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img729.png"
 ALT="$W^n$">|; 

$key = q/{displaymath}=mathrm{re}left[{{1over{1-{P}{Z^{-1}}}}{A{Z^n}}+{1over{1-overline{P}{Z^{-1}}}}{A{Z^n}}}right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img902.png"
 ALT="\begin{displaymath}
=
\mathrm{re} \left[ {
{1 \over {1 - {P}{Z^{-1}}}} {A{Z^n}} +
{1 \over {1 - \overline{P}{Z^{-1}}}} {A{Z^n}}
} \right ]
\end{displaymath}">|; 

$key = q/{displaymath}C[m]=S[m,k]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1153.png"
 ALT="\begin{displaymath}
C[m] = S[m, k]
\end{displaymath}">|; 

$key = q/2pislashomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$2 \pi / \omega$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="354" HEIGHT="242" BORDER="0"
 SRC="|."$dir".q|img583.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.05.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{switch}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img836.png"
 ALT="\fbox{$\mathrm{switch}\sim$}">|; 

$key = q/R(S(Z));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img966.png"
 ALT="$R(S(Z))$">|; 

$key = q/{displaymath}A=a+bi=rcdot(cos(alpha)+isin(alpha)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="238" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img873.png"
 ALT="\begin{displaymath}
A = a+bi = r \cdot (\cos(\alpha) + i \sin(\alpha))
\end{displaymath}">|; 

$key = q/{displaymath}+{J_1}(a)cos((omega_c+omega_m)n+{piover2})+{J_1}(a)cos((omega_c-omega_m)n+{piover2}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="401" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img537.png"
 ALT="\begin{displaymath}
+ {J_1}(a) \cos( (\omega_c+\omega_m) n + {\pi\over2})
+ {J_1}(a) \cos( (\omega_c-\omega_m) n + {\pi\over2})
\end{displaymath}">|; 

$key = q/Z_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img640.png"
 ALT="$Z_2$">|; 

$key = q/{displaymath}Y[n]cdotg{Z^{-d}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img718.png"
 ALT="\begin{displaymath}
Y[n] \cdot g{Z^{-d}}
\end{displaymath}">|; 

$key = q/{{a^2}slash2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img994.png"
 ALT="${{a^2} / 2}$">|; 

$key = q/{displaymath}x[n]approx{8over{{pi^2}}}left[{cos(omegan)}+{{cos(3omegan)}over9}+{{cos(5omegan)}over25}+cdotsright]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="345" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img1341.png"
 ALT="\begin{displaymath}
x[n] \approx {8 \over {{\pi^2}}} \left [
{\cos ( \omega n ...
...over 9}
+ {{\cos ( 5 \omega n)} \over 25}
+ \cdots
\right ]
\end{displaymath}">|; 

$key = q/x[n],n=0,...,N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="$x[n], n = 0, ..., N-1$">|; 

$key = q/{displaymath}(k+q)*{omega}={omega_c}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img591.png"
 ALT="\begin{displaymath}
(k + q) * {\omega} = {\omega_c}
\end{displaymath}">|; 

$key = q/{displaymath}pm(1-g)approxmathrm{im}({gW^{-d}})approxangle({W^{-d}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="231" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img734.png"
 ALT="\begin{displaymath}
\pm(1-g) \approx \mathrm{im}({gW^{-d}}) \approx \angle({W^{-d}})
\end{displaymath}">|; 

$key = q/{displaymath}{P_1}=(1-beta)(cosomega+isinomega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img921.png"
 ALT="\begin{displaymath}
{P_1} = (1 - \beta) (\cos \omega + i \sin \omega)
\end{displaymath}">|; 

$key = q/1-r;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img870.png"
 ALT="$1-r$">|; 

$key = q/x[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$x[n]$">|; 

$key = q/Z_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img639.png"
 ALT="$Z_1$">|; 

$key = q/t_3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="$t_3$">|; 

$key = q/1-1slashn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img975.png"
 ALT="$1-1/n$">|; 

$key = q/N=100;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="$N=100$">|; 

$key = q/t[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img318.png"
 ALT="$t[n]$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.01.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="254" HEIGHT="205" BORDER="0"
 SRC="|."$dir".q|img628.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.01.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig02.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="471" HEIGHT="664" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.02.ps}\end{figure}">|; 

$key = q/2(N-1)pislashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1044.png"
 ALT="$2(N-1)\pi/N$">|; 

$key = q/{displaymath}Z=a+bi{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="72" HEIGHT="25" BORDER="0"
 SRC="|."$dir".q|img624.png"
 ALT="\begin{displaymath}
Z = a + bi
\end{displaymath}">|; 

$key = q/fbox{texttt{rpole~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1030.png"
 ALT="\fbox{ \texttt{rpole\&nbsp;}}">|; 

$key = q/{displaymath}ldots,,(t[0],x[0]),,(t[1],x[1]),,ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="202" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img317.png"
 ALT="\begin{displaymath}
\ldots ,   (t[0], x[0]),   (t[1], x[1]),   \ldots
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig01.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="566" HEIGHT="180" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.13.ps}\end{figure}">|; 

$key = q/N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="$N$">|; 

$key = q/fbox{texttt{cpole~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1036.png"
 ALT="\fbox{ \texttt{cpole\&nbsp;}}">|; 

$key = q/{displaymath}(1-Q{Z^{-1}}){Z^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img862.png"
 ALT="\begin{displaymath}
(1 - Q{Z^{-1}}){Z^n}
\end{displaymath}">|; 

$key = q/1,Z,{Z^2},ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img664.png"
 ALT="$1, Z, {Z^2}, \ldots$">|; 

$key = q/{displaymath}X[n+Nslash2]=A[0]-A[1]{U^n}+A[2]{U^{2n}}pmcdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1256.png"
 ALT="\begin{displaymath}
X[n+N/2] = A[0] - A[1]{U^n} + A[2]{U^{2n}} \pm \cdots
\end{displaymath}">|; 

$key = q/fbox{texttt{czero~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1034.png"
 ALT="\fbox{ \texttt{czero\&nbsp;}}">|; 

$key = q/{displaymath}scdotx[n+1]-scdotx[n]={{sf}overR}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img812.png"
 ALT="\begin{displaymath}
s \cdot x[n+1] - s \cdot x[n] = {{sf} \over R}
\end{displaymath}">|; 

$key = q/-sslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img213.png"
 ALT="$-s/2$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.18.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="476" HEIGHT="240" BORDER="0"
 SRC="|."$dir".q|img622.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.18.ps}\end{figure}">|; 

$key = q/{displaymath}y[n]={{left({{n}over{N}}right)}^4},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img360.png"
 ALT="\begin{displaymath}
y[n] = {{ \left ( {{n} \over {N}} \right ) } ^ 4} ,
\end{displaymath}">|; 

$key = q/{displaymath}t={2^{hslash12}}={e^{log(2)slash12cdoth}}approx{e^{0.05776h}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="24" BORDER="0"
 SRC="|."$dir".q|img850.png"
 ALT="\begin{displaymath}
t = {2 ^ {h/12}} = {e ^ {\log(2)/12 \cdot h}} \approx {e ^ {0.05776 h}}
\end{displaymath}">|; 

$key = q/{displaymath}a=mathrm{re}(Z){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img626.png"
 ALT="\begin{displaymath}
a = \mathrm{re}(Z)
\end{displaymath}">|; 

$key = q/fslashR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img810.png"
 ALT="$f/R$">|; 

$key = q/{displaymath}x[n]=mathrm{re}(X[n]){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="105" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1003.png"
 ALT="\begin{displaymath}
x[n] = \mathrm{re} (X[n])
\end{displaymath}">|; 

$key = q/V=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1088.png"
 ALT="$V=1$">|; 

$key = q/fbox{{mathrm{sel}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img343.png"
 ALT="\fbox{ $\mathrm{sel}$ }">|; 

$key = q/{figure}{psfig{file=figsslashfig08.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="326" BORDER="0"
 SRC="|."$dir".q|img856.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.03.ps}\end{figure}">|; 

$key = q/{displaymath}h=12,{log_2}left({NoverM}right)=12,{log_2}left({NfoverR}right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="241" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img196.png"
 ALT="\begin{displaymath}
h = 12   {\log _ 2} \left ( {N \over M} \right ) =
12   {\log _ 2} \left ( {N f \over R} \right )
\end{displaymath}">|; 

$key = q/z[1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$z[1]$">|; 

$key = q/{displaymath}t={NslashM}={{Nf}slashR}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="130" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img195.png"
 ALT="\begin{displaymath}
t = {N / M} = {{N f} / R}
\end{displaymath}">|; 

$key = q/({x_1},ldots,{x_r});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="83" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img744.png"
 ALT="$({x_1}, \ldots, {x_r})$">|; 

$key = q/{figure}{psfig{file=figsslashfig10.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="376" BORDER="0"
 SRC="|."$dir".q|img1372.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.10.ps}\end{figure}">|; 

$key = q/{displaymath}{m_a}[n]={e^{acdot(cos(omegan)-1))}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img564.png"
 ALT="\begin{displaymath}
{m_a}[n] = {e^{a \cdot (\cos(\omega n) - 1))}}
\end{displaymath}">|; 

$key = q/{displaymath}(1-x[n])y[n]+x[n]z[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img188.png"
 ALT="\begin{displaymath}
(1 - x[n])y[n] + x[n]z[n]
\end{displaymath}">|; 

$key = q/-1slashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1294.png"
 ALT="$-1/N$">|; 

$key = q/-2slash(N-2M);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="103" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1345.png"
 ALT="$-2/(N-2M)$">|; 

$key = q/G;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img571.png"
 ALT="$G$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.26.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="273" HEIGHT="155" BORDER="0"
 SRC="|."$dir".q|img827.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.26.ps}\end{figure}">|; 

$key = q/X[-n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1267.png"
 ALT="$X[-n]$">|; 

$key = q/ktau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img481.png"
 ALT="$k \tau$">|; 

$key = q/kneq0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1317.png"
 ALT="$k \neq 0$">|; 

$key = q/({L_1},{d_1})=(0.3N,-0.3);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1283.png"
 ALT="$({L_1}, {d_1}) = (0.3N, -0.3)$">|; 

$key = q/{displaymath}{A_{mathrm{RMS}}}{x[n]}+{A_{mathrm{RMS}}}{y[n]}ge{A_{mathrm{RMS}}}{x[n]+y[n]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="337" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="\begin{displaymath}
{A_{\mathrm{RMS}}} \{x[n]\} +
{A_{\mathrm{RMS}}} \{y[n]\} \ge
{A_{\mathrm{RMS}}} \{x[n]+y[n]\}
\end{displaymath}">|; 

$key = q/{displaymath}xi=cos(pikslashN)-isin(pikslashN){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1082.png"
 ALT="\begin{displaymath}
\xi = \cos(\pi k / N) - i \sin(\pi k / N)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig09.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="530" HEIGHT="293" BORDER="0"
 SRC="|."$dir".q|img1215.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.14.ps}\end{figure}">|; 

$key = q/islash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1041.png"
 ALT="$i/2$">|; 

$key = q/{displaymath}X'[n]=aleft(cos(omegan)-isin(omegan)right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="214" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1005.png"
 ALT="\begin{displaymath}
X'[n] = a \left ( \cos (\omega n) - i \sin (\omega n) \right )
\end{displaymath}">|; 

$key = q/{displaymath}H(Z)=1-Q{Z^{-1}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="128" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img863.png"
 ALT="\begin{displaymath}
H(Z) = 1 - Q{Z^{-1}}
\end{displaymath}">|; 

$key = q/{displaymath}={{left[{U^{-k}}right]}^{0}}X[0]+{{left[{U^{-k}}right]}^{1}}X[1]+cdots+{{left[{U^{-k}}right]}^{N-1}}X[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="393" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1065.png"
 ALT="\begin{displaymath}
= {{\left [ {U^{-k}} \right ]} ^ {0}} X[0] +
{{\left [ {U^...
...X[1] +
\cdots +
{{\left [ {U^{-k}} \right ]} ^ {N-1}} X[N-1]
\end{displaymath}">|; 

$key = q/{displaymath}f(t)={1over2}-{1overpi}{left(sin(omegat)+{{sin(2omegat)}over2}+{{sin(3omegat)}over3}+cdotsright)}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="357" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img308.png"
 ALT="\begin{displaymath}
f(t) = {1 \over 2} - {1 \over \pi}
{ \left (
\sin(\omega ...
...\over 2} +
{{\sin(3 \omega t)} \over 3} + \cdots
\right ) }
\end{displaymath}">|; 

$key = q/{f_0}=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img514.png"
 ALT="${f_0}=0$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="444" HEIGHT="656" BORDER="0"
 SRC="|."$dir".q|img486.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.09.ps}\end{figure}">|; 

$key = q/|S[m,k]|-f[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1168.png"
 ALT="$\vert S[m, k]\vert-f[k]$">|; 

$key = q/g[m]C[m];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1160.png"
 ALT="$g[m]C[m]$">|; 

$key = q/{displaymath}{calFT}{x[n]-x[n-1]}approxiomegak{calFT}{x[n]}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="257" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1310.png"
 ALT="\begin{displaymath}
{\cal FT}\{ x[n] - x[n-1] \} \approx i \omega k {\cal FT}\{ x[n] \}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.27.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="558" HEIGHT="252" BORDER="0"
 SRC="|."$dir".q|img832.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.27.ps}\end{figure}">|; 

$key = q/{displaymath}H{Z^N}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="24" BORDER="0"
 SRC="|."$dir".q|img685.png"
 ALT="\begin{displaymath}
H {Z^N}
\end{displaymath}">|; 

$key = q/0<=n<Nslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1336.png"
 ALT="$0 &lt;= n &lt; N/2$">|; 

$key = q/-komega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1055.png"
 ALT="$-k\omega$">|; 

$key = q/omega_cn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img543.png"
 ALT="$\omega_c n$">|; 

$key = q/{displaymath}Z=cos(alpha)+isin(alpha){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1110.png"
 ALT="\begin{displaymath}
Z = \cos(\alpha) + i \sin(\alpha)
\end{displaymath}">|; 

$key = q/fbox{texttt{tabreceive~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1221.png"
 ALT="\fbox{\texttt{tabreceive\&nbsp;}}">|; 

$key = q/{displaymath}H={Z^{-dslash2}}({Z^{dslash2}}+{Z^{-dslash2}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img696.png"
 ALT="\begin{displaymath}
H = {Z^{-d/2}} ({Z^{d/2}} + {Z^{-d/2}})
\end{displaymath}">|; 

$key = q/{displaymath}y[n]=f(nslashN).{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="104" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img366.png"
 ALT="\begin{displaymath}
y[n] = f(n/N) .
\end{displaymath}">|; 

$key = q/{displaymath}Y[k]={calFT}left{X[n]right}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1064.png"
 ALT="\begin{displaymath}
Y[k] = {\cal FT}\left \{ X[n] \right \} (k)
\end{displaymath}">|; 

$key = q/fbox{texttt{rifft~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1224.png"
 ALT="\fbox{\texttt{rifft\&nbsp;}}">|; 

$key = q/{displaymath}H=1+{Z^{-d}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="25" BORDER="0"
 SRC="|."$dir".q|img687.png"
 ALT="\begin{displaymath}
H = 1 + {Z^{-d}}
\end{displaymath}">|; 

$key = q/k=0,...,N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="110" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1063.png"
 ALT="$k = 0, ..., N-1$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="646" HEIGHT="413" BORDER="0"
 SRC="|."$dir".q|img1223.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.15.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig09.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="448" HEIGHT="175" BORDER="0"
 SRC="|."$dir".q|img1100.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.02.ps}\end{figure}">|; 

$key = q/{displaymath}x[n]=acdotcos(omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1001.png"
 ALT="\begin{displaymath}
x[n] = a \cdot \cos (\omega n)
\end{displaymath}">|; 

$key = q/H(R(S(Z)));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img961.png"
 ALT="$H(R(S(Z)))$">|; 

$key = q/1-aomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img803.png"
 ALT="$1 - a \omega$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="332" HEIGHT="530" BORDER="0"
 SRC="|."$dir".q|img357.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.02.ps}\end{figure}">|; 

$key = q/phi=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="$\phi=0$">|; 

$key = q/{displaymath}x[n]=cos(omega_cn)f(acos(omega_mn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img552.png"
 ALT="\begin{displaymath}
x[n] = \cos(\omega_c n) f (a \cos(\omega_m n))
\end{displaymath}">|; 

$key = q/r=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img929.png"
 ALT="$r=0$">|; 

$key = q/g(x)=1-1slashx;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1170.png"
 ALT="$g(x) = 1-1/x$">|; 

$key = q/{displaymath}={{sin(omegan)}over{pi}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1323.png"
 ALT="\begin{displaymath}
= {{\sin ( \omega n)} \over {\pi}}
\end{displaymath}">|; 

$key = q/1slashk;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$1/k$">|; 

$key = q/{figure}{psfig{file=figsslashfig10.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="480" HEIGHT="344" BORDER="0"
 SRC="|."$dir".q|img1369.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.08.ps}\end{figure}">|; 

$key = q/f(x)={e^x};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img563.png"
 ALT="$f(x) = {e^x}$">|; 

$key = q/{displaymath}n>y[n]>n-D.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="124" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img790.png"
 ALT="\begin{displaymath}
n &gt; y[n] &gt; n - D.
\end{displaymath}">|; 

$key = q/705600-20000=685600;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="179" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1367.png"
 ALT="$705600-20000=685600$">|; 

$key = q/fbox{{mathrm{snapshot}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="97" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img348.png"
 ALT="\fbox{ $\mathrm{snapshot}\sim$}">|; 

$key = q/{displaymath}a=rcos(theta){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img635.png"
 ALT="\begin{displaymath}
a = r \cos (\theta)
\end{displaymath}">|; 

$key = q/sqrt{10};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$\sqrt {10}$">|; 

$key = q/{displaymath}x[n]={a_0}+{a_1}cosleft(omegan+{phi_1}right)+{a_2}cosleft(2omegan+{phi_2}right)+cdots+{a_p}cosleft(pomegan+{phi_p}right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="507" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="\begin{displaymath}
x[n] = {a_0} +
{a_1} \cos \left ( \omega n + {\phi_1} \rig...
... + \cdots +
{a_p} \cos \left ( p \omega n + {\phi_p} \right )
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="454" HEIGHT="259" BORDER="0"
 SRC="|."$dir".q|img885.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.11.ps}\end{figure}">|; 

$key = q/{A_k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1051.png"
 ALT="${A_k}$">|; 

$key = q/1slashf[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1238.png"
 ALT="$1/f[k]$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="431" HEIGHT="413" BORDER="0"
 SRC="|."$dir".q|img431.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.04.ps}\end{figure}">|; 

$key = q/d_1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1280.png"
 ALT="$d_1$">|; 

$key = q/fbox{texttt{bp~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1017.png"
 ALT="\fbox{ \texttt{bp\&nbsp;}}">|; 

$key = q/{displaymath}H(Z)={{1+{Z^{-1}}}over{1-g{Z^{-1}}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img947.png"
 ALT="\begin{displaymath}
H(Z) =
{{
1 + {Z^{-1}}
} \over {
1 - g{Z^{-1}}
}}
\end{displaymath}">|; 

$key = q/c[k]slashf[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1239.png"
 ALT="$c[k]/f[k]$">|; 

$key = q/{L_1},ldots,{L_j};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1278.png"
 ALT="${L_1}, \ldots, {L_j}$">|; 

$key = q/{figure}{psfig{file=figsslashfig02.08.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="603" HEIGHT="402" BORDER="0"
 SRC="|."$dir".q|img220.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.08.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{cpole}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1039.png"
 ALT="\fbox{$\mathrm{cpole}\sim$}">|; 

$key = q/fbox{{mathrm{inlet}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img375.png"
 ALT="\fbox{ $ \mathrm{inlet}\sim $}">|; 

$key = q/{displaymath}|H|={1over{|1-g{Z^{-d}}|}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img722.png"
 ALT="\begin{displaymath}
\vert H\vert = {1 \over {\vert 1 - g{Z^{-d}}\vert}}
\end{displaymath}">|; 

$key = q/{displaymath}|H|={1over{1-g}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img728.png"
 ALT="\begin{displaymath}
\vert H\vert = {1 \over {1 - g}}
\end{displaymath}">|; 

$key = q/2omega,4omega,6omega,ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img707.png"
 ALT="$2\omega, 4\omega, 6\omega, \ldots$">|; 

$key = q/{figure}{psfig{file=figsslashfig01.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="528" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.06.ps}\end{figure}">|; 

$key = q/{displaymath}-sin(omega_cn)*sin(acos(omega_mn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="194" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img472.png"
 ALT="\begin{displaymath}
- \sin(\omega_c n) * \sin(a \cos(\omega_m n))
\end{displaymath}">|; 

$key = q/{displaymath}h(bsin({omegaover2}n))=Gcdotleft({1over2}+Hcos(omegan)+{H^2}cos(2omegan)+cdotsright){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="397" HEIGHT="45" BORDER="0"
 SRC="|."$dir".q|img570.png"
 ALT="\begin{displaymath}
h(b \sin({\omega \over 2} n)) =
G \cdot \left (
{1\over 2...
...H \cos(\omega n) + {H^2} \cos(2 \omega n)
+ \cdots
\right )
\end{displaymath}">|; 

$key = q/1slashf;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img241.png"
 ALT="$1/f$">|; 

$key = q/{displaymath}X[-n]=A[0]+A[1](cos(omegan)-isin(omegan))+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1269.png"
 ALT="\begin{displaymath}
X[-n] =
A[0] + A[1](\cos(\omega n) - i \sin(\omega n)) + \cdots
\end{displaymath}">|; 

$key = q/N+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img265.png"
 ALT="$N+1$">|; 

$key = q/{displaymath}omega_m,3omega_m,5omega_m,ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="120" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img478.png"
 ALT="\begin{displaymath}
\omega_m, 3\omega_m, 5\omega_m, \ldots
\end{displaymath}">|; 

$key = q/Z^{-d};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img694.png"
 ALT="$Z^{-d}$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="390" HEIGHT="782" BORDER="0"
 SRC="|."$dir".q|img418.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.03.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{pipe}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img340.png"
 ALT="\fbox{ $\mathrm{pipe}$ }">|; 

$key = q/x[n]^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img989.png"
 ALT="$x[n]^2$">|; 

$key = q/{displaymath}Z={{pmasqrt{-W}-b}over{mpbsqrt{-W}+a}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="46" BORDER="0"
 SRC="|."$dir".q|img970.png"
 ALT="\begin{displaymath}
Z = { {
\pm a \sqrt { - W }
- b
} \over {
\mp b \sqrt { - W }
+ a
}
}
\end{displaymath}">|; 

$key = q/n+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img246.png"
 ALT="$n+1$">|; 

$key = q/y[n]=nslash(10R);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="109" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img359.png"
 ALT="$y[n] = n/(10R)$">|; 

$key = q/{D_N}(k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1090.png"
 ALT="${D_N}(k)$">|; 

$key = q/{displaymath}|1-Q{Z^{-1}}|=|Z||1-Q{Z^{-1}}|=|Q-Z|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="268" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img865.png"
 ALT="\begin{displaymath}
\vert 1 - Q{Z^{-1}}\vert = \vert Z\vert\vert 1 - Q{Z^{-1}}\vert = \vert Q - Z\vert
\end{displaymath}">|; 

$key = q/alpha+beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img419.png"
 ALT="$\alpha + \beta$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.16.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="548" HEIGHT="323" BORDER="0"
 SRC="|."$dir".q|img616.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.16.ps}\end{figure}">|; 

$key = q/y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$y$">|; 

$key = q/{displaymath}S[m,k];=;{{left|R'[k]right|}^{-1}};cdot;{{R'[k]T'[k]}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1207.png"
 ALT="\begin{displaymath}
S[m, k] \; = \;
{
{ \left \vert
R'[k]
\right \vert}
^
{-1}
}
\; \cdot \;
{
{R'[k] T'[k]}
}
\end{displaymath}">|; 

$key = q/{displaymath}left[2acos(alphan)right]cdotleft[cos(betan)right]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="152" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img417.png"
 ALT="\begin{displaymath}
\left [ 2 a \cos (\alpha n) \right ]
\cdot
\left [ \cos (\beta n) \right ]
\end{displaymath}">|; 

$key = q/beta=3pislash10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="$\beta =3\pi /10$">|; 

$key = q/alpha>beta>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\alpha &gt; \beta &gt; 0$">|; 

$key = q/|T[m,k]|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1174.png"
 ALT="$\vert T[m, k]\vert$">|; 

$key = q/y[n]=n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img203.png"
 ALT="$y[n] = n$">|; 

$key = q/f(x+y);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img447.png"
 ALT="$f(x+y)$">|; 

$key = q/alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\alpha $">|; 

$key = q/{figure}{psfig{file=figsslashfig04.17.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="487" HEIGHT="376" BORDER="0"
 SRC="|."$dir".q|img385.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.17.ps}\end{figure}">|; 

$key = q/{displaymath}{y_2}[n]=s{x_1}[n]-c{x_2}[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img760.png"
 ALT="\begin{displaymath}
{y_2}[n] = s {x_1}[n] - c {x_2}[n]
\end{displaymath}">|; 

$key = q/{displaymath}x[n]={{N^2}over{MN-2{M^2}}}(p[n-M]-p[n+M]){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="291" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1346.png"
 ALT="\begin{displaymath}
x[n] = {{N^2} \over {MN - 2{M^2}}} (p[n-M] - p[n+M])
\end{displaymath}">|; 

$key = q/fbox{texttt{clip~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img491.png"
 ALT="\fbox{ \texttt{clip\&nbsp;}}">|; 

$key = q/{displaymath}Y[n]=X[n]+Y[n]cdotg{Z^{-d}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img719.png"
 ALT="\begin{displaymath}
Y[n] = X[n]+Y[n] \cdot g{Z^{-d}}
\end{displaymath}">|; 

$key = q/{f_1}=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img515.png"
 ALT="${f_1}=1$">|; 

$key = q/{displaymath}{Z^{dslash2}}+{Z^{-dslash2}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="25" BORDER="0"
 SRC="|."$dir".q|img698.png"
 ALT="\begin{displaymath}
{Z^{d/2}} + {Z^{-d/2}}
\end{displaymath}">|; 

$key = q/{displaymath}f(acos(omegan))={{{e^{acos(omegan)}}}over{e^a}}={e^{a(cos(omegan)-1)}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="275" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img523.png"
 ALT="\begin{displaymath}
f(a \cos(\omega n)) =
{{{e^{a \cos(\omega n)}}} \over {e^a}} = {e^{a (\cos(\omega n) - 1)}}
\end{displaymath}">|; 

$key = q/l+s;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img211.png"
 ALT="$l+s$">|; 

$key = q/cos(omegan);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img450.png"
 ALT="$\cos(\omega n)$">|; 

$key = q/f();MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="$f()$">|; 

$key = q/{x_2}[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img746.png"
 ALT="${x_2}[n]$">|; 

$key = q/x^3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img498.png"
 ALT="$x^3$">|; 

$key = q/mtau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img482.png"
 ALT="$m \tau$">|; 

$key = q/x[1.5];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img795.png"
 ALT="$x[1.5]$">|; 

$key = q/(a,b);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img630.png"
 ALT="$(a,b)$">|; 

$key = q/b[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1012.png"
 ALT="$b[n]$">|; 

$key = q/{displaymath}={V^d}{calFT}left{X[n]right}(k){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1105.png"
 ALT="\begin{displaymath}
= {V^d} {\cal FT} \left \{ X[n] \right \} (k)
\end{displaymath}">|; 

$key = q/fbox{{mathrm{catchsim}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img387.png"
 ALT="\fbox{$\mathrm{catch\sim}$}">|; 

$key = q/omega_m=komega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img484.png"
 ALT="$\omega_m=k\omega$">|; 

$key = q/fbox{{mathrm{until}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img623.png"
 ALT="\fbox{ $\mathrm{until}$ }">|; 

$key = q/M+N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$M+N-1$">|; 

$key = q/{displaymath}cos(5omegan){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img495.png"
 ALT="\begin{displaymath}
\cos(5 \omega n)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.23.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="319" HEIGHT="218" BORDER="0"
 SRC="|."$dir".q|img985.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.23.ps}\end{figure}">|; 

$key = q/{displaymath}t=p+cf{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img294.png"
 ALT="\begin{displaymath}
t = p + cf
\end{displaymath}">|; 

$key = q/a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$a$">|; 

$key = q/{displaymath}y[n]=pcdoty[n-1]+(1-p)cdotx[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="226" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img988.png"
 ALT="\begin{displaymath}
y[n] = p \cdot y[n-1] + (1-p) \cdot x[n]
\end{displaymath}">|; 

$key = q/-domegaslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img697.png"
 ALT="$-d \omega / 2$">|; 

$key = q/y[n]cdotx[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$y[n] \cdot x[n]$">|; 

$key = q/{displaymath}t[n]=left|y[n]-y[n-1]right|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img200.png"
 ALT="\begin{displaymath}
t[n] = \left \vert y[n] - y[n-1] \right \vert
\end{displaymath}">|; 

$key = q/f(0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img562.png"
 ALT="$f(0)$">|; 

$key = q/fbox{texttt{block~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img833.png"
 ALT="\fbox{ \texttt{block\&nbsp;}}">|; 

$key = q/{figure}{psfig{file=figsslashfig05.05.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="172" HEIGHT="226" BORDER="0"
 SRC="|."$dir".q|img432.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.05.ps}\end{figure}">|; 

$key = q/{displaymath}{calFT}left{{Z^n}right}(k)={calFT}left{1right}(k-{{alpha}over{omega}}){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="218" HEIGHT="35" BORDER="0"
 SRC="|."$dir".q|img1116.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ {Z^n} \right \} (k) =
{\cal FT} \left \{ 1 \right \}(k - {{\alpha } \over {\omega}})
\end{displaymath}">|; 

$key = q/fbox{texttt{lop~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1014.png"
 ALT="\fbox{\texttt{lop\&nbsp;}}">|; 

$key = q/p[n+M];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1349.png"
 ALT="$p[n+M]$">|; 

$key = q/1-q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img603.png"
 ALT="$1-q$">|; 

$key = q/0lex[n]le1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$0 \le x[n] \le 1$">|; 

$key = q/{displaymath}s=sin(theta){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img751.png"
 ALT="\begin{displaymath}
s = \sin(\theta)
\end{displaymath}">|; 

$key = q/omega_p;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img541.png"
 ALT="$\omega_p$">|; 

$key = q/{displaymath}f(x[n])={{a^2}over2}left(1+cos(2alphan)right)+{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="208" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img438.png"
 ALT="\begin{displaymath}
f(x[n]) = {{a^2} \over 2} \left ( 1 + \cos(2 \alpha n) \right ) +
\end{displaymath}">|; 

$key = q/x<1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1171.png"
 ALT="$x&lt;1$">|; 

$key = q/fbox{texttt{lrshift~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1241.png"
 ALT="\fbox{\texttt{lrshift\&nbsp;}}">|; 

$key = q/2alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img993.png"
 ALT="$2 \alpha$">|; 

$key = q/fbox{{mathrm{line}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img345.png"
 ALT="\fbox{ $\mathrm{line}$}">|; 

$key = q/angle(A+B);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img668.png"
 ALT="$\angle(A+B)$">|; 

$key = q/a[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="30" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img503.png"
 ALT="$a[n]$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.17.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="482" HEIGHT="525" BORDER="0"
 SRC="|."$dir".q|img621.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.17.ps}\end{figure}">|; 

$key = q/g[m,k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1164.png"
 ALT="$g[m, k]$">|; 

$key = q/Rslash30;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img816.png"
 ALT="$R/30$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.11.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="310" HEIGHT="230" BORDER="0"
 SRC="|."$dir".q|img608.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.11.ps}\end{figure}">|; 

$key = q/komega=2pikslashN;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1307.png"
 ALT="$k \omega = 2\pi k / N$">|; 

$key = q/{figure}{psfig{file=figsslashfig10.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="480" HEIGHT="109" BORDER="0"
 SRC="|."$dir".q|img1292.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.04.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="326" HEIGHT="137" BORDER="0"
 SRC="|."$dir".q|img702.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.06.ps}\end{figure}">|; 

$key = q/m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$m$">|; 

$key = q/Vnot=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1080.png"
 ALT="$V \not= 1$">|; 

$key = q/{displaymath}w[n]={1over2}-{1over4}{U^n}-{1over4}{U^{-n}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img1126.png"
 ALT="\begin{displaymath}
w[n] = {1\over 2} - {1\over 4} {U^n} - {1\over 4} {U^{-n}}
\end{displaymath}">|; 

$key = q/{displaymath}{Q_1}=qcdot(cosomega+isinomega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img926.png"
 ALT="\begin{displaymath}
{Q_1} = q \cdot (\cos \omega + i \sin \omega)
\end{displaymath}">|; 

$key = q/r=|Q|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="$r=\vert Q\vert$">|; 

$key = q/P;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img880.png"
 ALT="$P$">|; 

$key = q/f(x)={x^n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img400.png"
 ALT="$f(x) = {x^n}$">|; 

$key = q/{displaymath}S[k]=S[m,k]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1152.png"
 ALT="\begin{displaymath}
S[k] = S[m, k]
\end{displaymath}">|; 

$key = q/1slash50;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1365.png"
 ALT="$1/50$">|; 

$key = q/{displaymath}x[N],ldots,x[N+B-1]longrightarrow{fbox{texttt{delwrite~}}{{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="279" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img828.png"
 ALT="\begin{displaymath}
x[N], \ldots, x[N+B-1] \longrightarrow \fbox{\texttt{delwrite\&nbsp;}}
\end{displaymath}">|; 

$key = q/M(k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1132.png"
 ALT="$M(k)$">|; 

$key = q/{x_1},ldots{x_k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img766.png"
 ALT="${x_1}, \ldots {x_k}$">|; 

$key = q/{displaymath}{xi^N}-{xi^{-N}}=left(cos(pik)-isin(pik)right)-left(cos(pik)+isin(pik)right)=-2isin(pik){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="493" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1086.png"
 ALT="\begin{displaymath}
{\xi^N} - {\xi^{-N}} =
\left (\cos(\pi k) - i \sin(\pi k) ...
...eft (\cos(\pi k) + i \sin(\pi k) \right )
= - 2 i \sin(\pi k)
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="210" BORDER="0"
 SRC="|."$dir".q|img860.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.07.ps}\end{figure}">|; 

$key = q/{c_1},ldots,{c_l};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="64" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1296.png"
 ALT="${c_1}, \ldots, {c_l}$">|; 

$key = q/{D_n}(k);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1134.png"
 ALT="${D_n}(k)$">|; 

$key = q/{displaymath}{|{x_1}|}^2+cdots+{|{x_r}|}^2{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img743.png"
 ALT="\begin{displaymath}
{\vert{x_1}\vert}^2 + \cdots + {\vert{x_r}\vert}^2
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig06.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="352" HEIGHT="285" BORDER="0"
 SRC="|."$dir".q|img614.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.14.ps}\end{figure}">|; 

$key = q/y[n]=2n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="69" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img206.png"
 ALT="$y[n] = 2n$">|; 

$key = q/{figure}{psfig{file=figsslashfig02.15.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="546" HEIGHT="547" BORDER="0"
 SRC="|."$dir".q|img281.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.15.ps}\end{figure}">|; 

$key = q/angle(H(omega));MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img854.png"
 ALT="$\angle( H(\omega))$">|; 

$key = q/x=|S[m,k]|slashf[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1169.png"
 ALT="$x = \vert S[m, k]\vert/f[k]$">|; 

$key = q/{figure}{psfig{file=figsslashfig10.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="524" HEIGHT="396" BORDER="0"
 SRC="|."$dir".q|img1375.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.12.ps}\end{figure}">|; 

$key = q/{displaymath}(1-g)slashd{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img735.png"
 ALT="\begin{displaymath}
(1-g)/d
\end{displaymath}">|; 

$key = q/p=1-omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img911.png"
 ALT="$p = 1-\omega$">|; 

$key = q/N+3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img270.png"
 ALT="$N+3$">|; 

$key = q/0:1:2:cdots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="85" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img403.png"
 ALT="$0:1:2:\cdots$">|; 

$key = q/|Z|=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\vert Z\vert=1$">|; 

$key = q/{displaymath}X[n]=A[0]+A[1](cos(omegan)+isin(omegan))+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="313" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1253.png"
 ALT="\begin{displaymath}
X[n] =
A[0] + A[1](\cos(\omega n) + i \sin(\omega n)) + \cdots
\end{displaymath}">|; 

$key = q/n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$n$">|; 

$key = q/{displaymath}{1overZ}={Z^{-1}}=cos(omega)-isin(omega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="199" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img656.png"
 ALT="\begin{displaymath}
{1 \over Z} = {Z^{-1}} = cos(\omega) - i \sin(\omega)
\end{displaymath}">|; 

$key = q/{displaymath}{J_3}(a)cos((omega_c+3omega_m)n+{{3pi}over2}+bcos(omega_pn)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="289" HEIGHT="38" BORDER="0"
 SRC="|."$dir".q|img545.png"
 ALT="\begin{displaymath}
{J_3}(a) \cos( (\omega_c+3\omega_m) n + {{3\pi}\over2} + b \cos(\omega_p n))
\end{displaymath}">|; 

$key = q/k=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img259.png"
 ALT="$k=1$">|; 

$key = q/fbox{{mathrm{lop}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1015.png"
 ALT="\fbox{$\mathrm{lop}\sim$}">|; 

$key = q/{displaymath}{calFT}left{X[n]right}(k)=left({{parbox[t][0.1in]{0in}{mbox{}}{cos((pik(N-1)slashN)}right){{sin(pik)}over{sin(pikslashN)}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="502" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1087.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ X[n] \right \} (k) =
\left ( {
\parbo...
...
} \right )
{{
\sin(\pi k)
} \over {
\sin(\pi k / N)
}}
\end{displaymath}">|; 

$key = q/fbox{texttt{rfft~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1218.png"
 ALT="\fbox{\texttt{rfft\&nbsp;}}">|; 

$key = q/C[m-1];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1161.png"
 ALT="$C[m-1]$">|; 

$key = q/{displaymath}{a_0}={10^{-5}}=0.00001{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="141" HEIGHT="26" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="\begin{displaymath}
{a_0} = {10^{-5}} = 0.00001
\end{displaymath}">|; 

$key = q/n-B;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img329.png"
 ALT="$n-B$">|; 

$key = q/N-3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img263.png"
 ALT="$N-3$">|; 

$key = q/{displaymath}+{{b^2}over2}left(1+cos(2betan)right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img439.png"
 ALT="\begin{displaymath}
+ {{b^2} \over 2} \left ( 1 + \cos(2 \beta n) \right )
\end{displaymath}">|; 

$key = q/x[n]=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$x[n] = 0$">|; 

$key = q/{M_i},ldots,{M_l};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="79" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1295.png"
 ALT="${M_i}, \ldots, {M_l}$">|; 

$key = q/{displaymath}ldots,A,AZ,A{Z^2},ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img659.png"
 ALT="\begin{displaymath}
\ldots, A, AZ, A{Z^2}, \ldots
\end{displaymath}">|; 

$key = q/X'[n]=X[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="94" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1263.png"
 ALT="$X'[n] = X[n]$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.02.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="491" HEIGHT="318" BORDER="0"
 SRC="|."$dir".q|img855.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.02.ps}\end{figure}">|; 

$key = q/{displaymath}{y_1}[n]=c{x_1}[n]-s{x_2}[n]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="156" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img747.png"
 ALT="\begin{displaymath}
{y_1}[n] = c {x_1}[n] - s {x_2}[n]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig06.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="436" HEIGHT="408" BORDER="0"
 SRC="|."$dir".q|img610.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.12.ps}\end{figure}">|; 

$key = q/MslashN=0.03;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$M/N=0.03$">|; 

$key = q/|1-Q{Z^{-1}}|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img867.png"
 ALT="$\vert 1 - Q{Z^{-1}}\vert$">|; 

$key = q/X;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img670.png"
 ALT="$X$">|; 

$key = q/{figure}{psfig{file=figsslashfig01.03.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="419" HEIGHT="267" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="\begin{figure}\psfig{file=figs/fig01.03.ps}\end{figure}">|; 

$key = q/yge0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$y \ge
0$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.21.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="281" HEIGHT="403" BORDER="0"
 SRC="|."$dir".q|img806.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.21.ps}\end{figure}">|; 

$key = q/m=ldots,0,1,ldots;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1148.png"
 ALT="$m = \ldots, 0, 1, \ldots$">|; 

$key = q/{displaymath}cos(acos(omegan))={J_0}(a)-2{J_2}(a)cos(2omegan)+2{J_4}(a)cos(4omegan)-2{J_6}(a)cos(6omegan)pmcdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="553" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img528.png"
 ALT="\begin{displaymath}
\cos(a \cos(\omega n)) = {J_0}(a)
- 2 {J_2}(a) \cos(2 \om...
...a) \cos(4 \omega n)
- 2 {J_6}(a) \cos(6 \omega n) \pm \cdots
\end{displaymath}">|; 

$key = q/{displaymath}f(x)={x^2}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img434.png"
 ALT="\begin{displaymath}
f(x) = {x^2}
\end{displaymath}">|; 

$key = q/{displaymath}ldots,cos(0),cos(omega),cos(2omega),ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="203" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img658.png"
 ALT="\begin{displaymath}
\ldots, \cos(0), \cos(\omega), \cos(2 \omega), \ldots
\end{displaymath}">|; 

$key = q/n=Nslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1246.png"
 ALT="$n=N/2$">|; 

$key = q/y[0];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="28" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="$y[0]$">|; 

$key = q/{figure}{psfig{file=figsslashfig03.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="338" HEIGHT="384" BORDER="0"
 SRC="|."$dir".q|img335.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.10.ps}\end{figure}">|; 

$key = q/1slash4;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1135.png"
 ALT="$1/4$">|; 

$key = q/{displaymath}p[n]={1over2}{{({noverN}-{1over2})}^2}-{1over{24}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="167" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img1293.png"
 ALT="\begin{displaymath}
p[n] = {1 \over 2} {{({n\over N} - {1\over 2})}^2} - {1 \over {24}}
\end{displaymath}">|; 

$key = q/fbox{{mathrm{block}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img835.png"
 ALT="\fbox{$\mathrm{block}\sim$}">|; 

$key = q/{displaymath}H=1+Hg{Z^{-d}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="115" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img721.png"
 ALT="\begin{displaymath}
H = 1 + Hg{Z^{-d}}
\end{displaymath}">|; 

$key = q/H(omega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img853.png"
 ALT="$H(\omega)$">|; 

$key = q/n=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="42" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img267.png"
 ALT="$n=1$">|; 

$key = q/k=3;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1178.png"
 ALT="$k=3$">|; 

$key = q/fbox{{mathrm{tabread4}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img276.png"
 ALT="\fbox{ $\mathrm{tabread4}\sim$ }">|; 

$key = q/n=0,...,N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="$n = 0, ..., N-1$">|; 

$key = q/q=1-dsqrt{g};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="89" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img917.png"
 ALT="$q = 1 - d \sqrt{g}$">|; 

$key = q/{displaymath}{{n}over{2pislashomega}}={{1}over{2pi}}{{omega}over{b}}={{q}over{2pi}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="136" HEIGHT="42" BORDER="0"
 SRC="|."$dir".q|img981.png"
 ALT="\begin{displaymath}
{{n} \over {2\pi/\omega}} = {{1} \over {2\pi}} {{\omega} \over {b}}
= {{q} \over {2\pi}}
\end{displaymath}">|; 

$key = q/{displaymath}={{left[{U^{0}}right]}^{k}}X[0]+{{left[{U^{-1}}right]}^{k}}X[1]+cdots+{{left[{U^{-(N-1)}}right]}^{k}}X[N-1]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1066.png"
 ALT="\begin{displaymath}
= {{\left [ {U^{0}} \right ]} ^ {k}} X[0] +
{{\left [ {U^{...
...1] +
\cdots +
{{\left [ {U^{-(N-1)}} \right ]} ^ {k}} X[N-1]
\end{displaymath}">|; 

$key = q/fbox{{mathrm{s}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img290.png"
 ALT="\fbox{ $\mathrm{s}\sim$ }">|; 

$key = q/N-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$N-1$">|; 

$key = q/{displaymath}0cdotx+1cdoty=1,{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img326.png"
 ALT="\begin{displaymath}
0 \cdot x + 1 \cdot y = 1,
\end{displaymath}">|; 

$key = q/m=60;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="54" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$m=60$">|; 

$key = q/fbox{{mathrm{rzero}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1031.png"
 ALT="\fbox{$\mathrm{rzero}\sim$}">|; 

$key = q/{displaymath}={V^d}left({V^{0}}X[0]+{V^{1}}X[1]+cdots+{V^{N-1}}X[N-1]right){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="336" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img1104.png"
 ALT="\begin{displaymath}
= {V^d} \left (
{V ^ {0}} X[0] +
{V ^ {1}} X[1] +
\cdots +
{V ^ {N-1}} X[N-1]
\right )
\end{displaymath}">|; 

$key = q/|C[m]|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1163.png"
 ALT="$\vert C[m]\vert$">|; 

$key = q/{displaymath}|overline{Q}-{Z^{-1}}|=|Q-overline{Z^{-1}}|=|Q-Z|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="232" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img876.png"
 ALT="\begin{displaymath}
\vert\overline{Q} - {Z^{-1}}\vert = \vert Q - \overline{Z^{-1}}\vert = \vert Q- Z\vert
\end{displaymath}">|; 

$key = q/fbox{{mathrm{makenote}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img399.png"
 ALT="\fbox{$\mathrm{makenote}$}">|; 

$key = q/f;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$f$">|; 

$key = q/{y_1},ldots{y_k};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img767.png"
 ALT="${y_1}, \ldots {y_k}$">|; 

$key = q/-59;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1143.png"
 ALT="$-59$">|; 

$key = q/n-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img252.png"
 ALT="$n-1$">|; 

$key = q/X[m];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1067.png"
 ALT="$X[m]$">|; 

$key = q/{displaymath}X[n]=A{Z^n}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="86" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img674.png"
 ALT="\begin{displaymath}
X[n] = A {Z^n}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.17.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="447" HEIGHT="405" BORDER="0"
 SRC="|."$dir".q|img785.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.17.ps}\end{figure}">|; 

$key = q/Rslash20;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$R/20$">|; 

$key = q/{displaymath}t=1+aomegacos(omegan-pislash2){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="174" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img802.png"
 ALT="\begin{displaymath}
t = 1 + a \omega \cos(\omega n - \pi/2)
\end{displaymath}">|; 

$key = q/pislash10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="37" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img223.png"
 ALT="$\pi/10$">|; 

$key = q/lfloortrfloor;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img322.png"
 ALT="$\lfloor t \rfloor$">|; 

$key = q/{displaymath}x[t]={J_0}(a)cos(omega_cn){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="142" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img536.png"
 ALT="\begin{displaymath}
x[t] = {J_0}(a) \cos( \omega_c n )
\end{displaymath}">|; 

$key = q/kapprox1slash(4cdot0.03)approx8.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="151" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1360.png"
 ALT="$k \approx 1/(4\cdot 0.03) \approx 8.5$">|; 

$key = q/sin(-domega);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img690.png"
 ALT="$\sin(-d \omega)$">|; 

$key = q/ycdotx[n];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$y \cdot
x[n]$">|; 

$key = q/M;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$M$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.21.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="387" HEIGHT="255" BORDER="0"
 SRC="|."$dir".q|img973.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.21.ps}\end{figure}">|; 

$key = q/omega_c=momega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img485.png"
 ALT="$\omega_c=m\omega$">|; 

$key = q/{figure}{psfig{file=figsslashfig08.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="243" BORDER="0"
 SRC="|."$dir".q|img859.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.06.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig03.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="475" HEIGHT="724" BORDER="0"
 SRC="|."$dir".q|img344.png"
 ALT="\begin{figure}\psfig{file=figs/fig03.13.ps}\end{figure}">|; 

$key = q/fbox{{mathrm{osc}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="57" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="\fbox{ $ \mathrm{osc}\sim $}">|; 

$key = q/{displaymath}x[n]=cos(omegacdot(n-1.5)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img794.png"
 ALT="\begin{displaymath}
x[n] = \cos(\omega \cdot (n - 1.5))
\end{displaymath}">|; 

$key = q/h;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img194.png"
 ALT="$h$">|; 

$key = q/b;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="10" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$b$">|; 

$key = q/{displaymath}cos(a+b)=cos(a)cos(b)-sin(a)sin(b){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="274" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img412.png"
 ALT="\begin{displaymath}
\cos(a+b) = \cos(a)\cos(b) - \sin(a) \sin(b)
\end{displaymath}">|; 

$key = q/W(phi)=(1+mathop{mathgroupsymoperatorscos}nolimits(phi))slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="162" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$W(\phi )=(1+\mathop {\mathgroup \symoperators cos}\nolimits (\phi ))/2$">|; 

$key = q/{displaymath}y[n]=a+(b-a){{n-M}overN},hspace{0.1in}MlenleM+N-1.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="342" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="\begin{displaymath}
y[n] = a + (b - a) {{n-M} \over N}, \hspace{0.1in} M \le n \le M+N-1.
\end{displaymath}">|; 

$key = q/d=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img736.png"
 ALT="$d=1$">|; 

$key = q/p=1-q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img619.png"
 ALT="$p=1-q$">|; 

$key = q/m-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1185.png"
 ALT="$m-1$">|; 

$key = q/{displaymath}={Nover{4{pi^2}{k^2}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="39" BORDER="0"
 SRC="|."$dir".q|img1332.png"
 ALT="\begin{displaymath}
= {N \over {4 {\pi ^2} {k^2}}}
\end{displaymath}">|; 

$key = q/k=2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1248.png"
 ALT="$k=2$">|; 

$key = q/g;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$g$">|; 

$key = q/beta-alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img422.png"
 ALT="$\beta-\alpha$">|; 

$key = q/({k^2}-k)slash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img442.png"
 ALT="$({k^2}-k)/2$">|; 

$key = q/{displaymath}{[{{(1-gcos(omegad))}^2}+{{(gsin(omegad))}^2}]}^{-1slash2}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="246" HEIGHT="30" BORDER="0"
 SRC="|."$dir".q|img851.png"
 ALT="\begin{displaymath}
{[ {{(1-g \cos (\omega d))}^2} + {{(g \sin (\omega d))}^2} ]}
^
{-1/2}
\end{displaymath}">|; 

$key = q/fbox{{mathrm{tabreceive}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="101" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1222.png"
 ALT="\fbox{$\mathrm{tabreceive}\sim$}">|; 

$key = q/{displaymath}Z=cos(omega)+isin(omega){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img652.png"
 ALT="\begin{displaymath}
Z = \cos(\omega) + i \sin(\omega)
\end{displaymath}">|; 

$key = q/overline{P};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img890.png"
 ALT="$\overline{P}$">|; 

$key = q/-dkomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1108.png"
 ALT="$-dk\omega$">|; 

$key = q/{displaymath}H(Z)=1-{{{1-p}over{1-p{Z^{-1}}}}}=p{{{1-{Z^{-1}}}over{1-p{Z^{-1}}}}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="252" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img912.png"
 ALT="\begin{displaymath}
H(Z) = 1 - {{{1-p} \over {1 - p{Z^{-1}}}}}
= p{{{1-{Z^{-1}}} \over {1 - p{Z^{-1}}}}}
\end{displaymath}">|; 

$key = q/|P|>1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img884.png"
 ALT="$\vert P\vert&gt; 1$">|; 

$key = q/2pi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$2\pi $">|; 

$key = q/{figure}{psfig{file=figsslashfig06.10.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="493" HEIGHT="466" BORDER="0"
 SRC="|."$dir".q|img607.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.10.ps}\end{figure}">|; 

$key = q/g[m];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1159.png"
 ALT="$g[m]$">|; 

$key = q/tau;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$\tau$">|; 

$key = q/{b^2}=2a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img566.png"
 ALT="${b^2}=2a$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.25.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="527" HEIGHT="425" BORDER="0"
 SRC="|."$dir".q|img824.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.25.ps}\end{figure}">|; 

$key = q/-42;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1140.png"
 ALT="$-42$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="368" BORDER="0"
 SRC="|."$dir".q|img436.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.07.ps}\end{figure}">|; 

$key = q/sqrt{2};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="37" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img732.png"
 ALT="$\sqrt{2}$">|; 

$key = q/X';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1258.png"
 ALT="$X'$">|; 

$key = q/l;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="8" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img210.png"
 ALT="$l$">|; 

$key = q/{figure}{psfig{file=figsslashfig06.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="322" HEIGHT="326" BORDER="0"
 SRC="|."$dir".q|img604.png"
 ALT="\begin{figure}\psfig{file=figs/fig06.09.ps}\end{figure}">|; 

$key = q/(kslashN)^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1309.png"
 ALT="$(k/N)^2$">|; 

$key = q/l+sslash2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img216.png"
 ALT="$l+s/2$">|; 

$key = q/x^k;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img506.png"
 ALT="$x^k$">|; 

$key = q/{displaymath}{D_N}(k)=left{array{{ll}N&{k=0}{{sin(pik)}over{sin(pikslashN)}}&{knot=0,;-N<k<N}array{right.{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="307" HEIGHT="54" BORDER="0"
 SRC="|."$dir".q|img1091.png"
 ALT="\begin{displaymath}
{D_N}(k) =
\left \{
\begin{array}{ll}
N &amp; {k= 0} \\\\
{...
...pi k / N)
}}
&amp; {k\not=0,\; -N &lt; k &lt; N}
\end{array} \right .
\end{displaymath}">|; 

$key = q/g=0.8;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$g = 0.8$">|; 

$key = q/c_0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img237.png"
 ALT="$c_0$">|; 

$key = q/t=fsslashR;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img209.png"
 ALT="$t = fs/R$">|; 

$key = q/|A+B|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img667.png"
 ALT="$\vert A+B\vert$">|; 

$key = q/{figure}{psfig{file=figsslashfig05.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="411" HEIGHT="313" BORDER="0"
 SRC="|."$dir".q|img494.png"
 ALT="\begin{figure}\psfig{file=figs/fig05.12.ps}\end{figure}">|; 

$key = q/{displaymath}{calFT}left{X[n]right}(k)={{{V^N}-1}over{V-1}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="177" HEIGHT="43" BORDER="0"
 SRC="|."$dir".q|img1081.png"
 ALT="\begin{displaymath}
{\cal FT} \left \{ X[n] \right \} (k) =
{{
{V^N} - 1
} \over {
V - 1
}}
\end{displaymath}">|; 

$key = q/{displaymath}=cos((pi-omega)n-phi){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img304.png"
 ALT="\begin{displaymath}
= \cos((\pi - \omega)n - \phi)
\end{displaymath}">|; 

$key = q/fbox{{mathrm{tabwrite}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img277.png"
 ALT="\fbox{ $\mathrm{tabwrite}\sim$ }">|; 

$key = q/({y_1},{y_2});MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="52" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img752.png"
 ALT="$({y_1}, {y_2})$">|; 

$key = q/{figure}{psfig{file=figsslashfig02.13.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="407" HEIGHT="687" BORDER="0"
 SRC="|."$dir".q|img275.png"
 ALT="\begin{figure}\psfig{file=figs/fig02.13.ps}\end{figure}">|; 

$key = q/X'';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1260.png"
 ALT="$X''$">|; 

$key = q/1slash(1-g);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="$1/(1-g)$">|; 

$key = q/{displaymath}X''[n]={{X[n]-X[n+Nslash2]}over2}=A[1]{U^n}+A[3]{U^{3n}}+cdots+A[N-1]{U^{(N-1)n}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="525" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1261.png"
 ALT="\begin{displaymath}
X''[n] = {{X[n] - X[n+N/2]}\over 2} =
A[1]{U^n} + A[3]{U^{3n}} + \cdots + A[N-1]{U^{(N-1)n}}
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig08.29.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="303" HEIGHT="355" BORDER="0"
 SRC="|."$dir".q|img1024.png"
 ALT="\begin{figure}\psfig{file=figs/fig08.29.ps}\end{figure}">|; 

$key = q/{displaymath}z[n]=x[y[n]]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="\begin{displaymath}
z[n] = x[y[n]]
\end{displaymath}">|; 

$key = q/{figure}{psfig{file=figsslashfig04.18.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="472" HEIGHT="394" BORDER="0"
 SRC="|."$dir".q|img391.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.18.ps}\end{figure}">|; 

$key = q/x[n-1.5];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img783.png"
 ALT="$x[n-1.5]$">|; 

$key = q/{figure}{psfig{file=figsslashfig10.09.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="474" HEIGHT="109" BORDER="0"
 SRC="|."$dir".q|img1370.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.09.ps}\end{figure}">|; 

$key = q/phi-xi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img427.png"
 ALT="$\phi - \xi$">|; 

$key = q/{displaymath}X'[n]={{X[n]+X[-n]}over2}=A[0]+A[1]cos(omegan)+cdots+A[N-1]cos(omega(N-1)n){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="544" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1272.png"
 ALT="\begin{displaymath}
X'[n] = {{X[n] + X[-n]}\over 2} =
A[0] + A[1]\cos(\omega n)+ \cdots + A[N-1]\cos(\omega (N-1) n)
\end{displaymath}">|; 

$key = q/10R;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img358.png"
 ALT="$10R$">|; 

$key = q/{figure}{psfig{file=figsslashfig09.04.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="440" HEIGHT="136" BORDER="0"
 SRC="|."$dir".q|img1122.png"
 ALT="\begin{figure}\psfig{file=figs/fig09.04.ps}\end{figure}">|; 

$key = q/{figure}{psfig{file=figsslashfig07.14.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="381" HEIGHT="287" BORDER="0"
 SRC="|."$dir".q|img765.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.14.ps}\end{figure}">|; 

$key = q/1<a<2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img511.png"
 ALT="$1&lt;a&lt;2$">|; 

$key = q/{figure}{psfig{file=figsslashfig04.12.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="222" HEIGHT="229" BORDER="0"
 SRC="|."$dir".q|img379.png"
 ALT="\begin{figure}\psfig{file=figs/fig04.12.ps}\end{figure}">|; 

$key = q/{displaymath}{a_0}+{a_1}cosleft(2omegan+{phi_1}right)+{a_2}cosleft(4omegan+{phi_2}right)+cdots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="327" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img228.png"
 ALT="\begin{displaymath}
{a_0} +
{a_1} \cos \left ( 2 \omega n + {\phi_1} \right ) +
{a_2} \cos \left ( 4 \omega n + {\phi_2} \right ) + \cdots
\end{displaymath}">|; 

$key = q/R(Z);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="40" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img939.png"
 ALT="$R(Z)$">|; 

$key = q/{displaymath}angleT[k+1]-angleT[k]=angleS[m-1,k+1]-angleS[m-1,k]{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="364" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img1201.png"
 ALT="\begin{displaymath}
\angle T[k+1] - \angle T[k] = \angle S[m-1, k+1] - \angle S[m-1, k]
\end{displaymath}">|; 

$key = q/omega_cn+bcos(omega_pn);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img544.png"
 ALT="$\omega_c n + b \cos(\omega_p n)$">|; 

$key = q/{displaymath}Q=rcdot(cos(alpha)+isin(alpha)){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="178" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img864.png"
 ALT="\begin{displaymath}
Q = r \cdot (\cos(\alpha) + i \sin(\alpha))
\end{displaymath}">|; 

$key = q/x[0];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img682.png"
 ALT="$x[0]$">|; 

$key = q/{figure}{psfig{file=figsslashfig10.06.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="473" HEIGHT="97" BORDER="0"
 SRC="|."$dir".q|img1334.png"
 ALT="\begin{figure}\psfig{file=figs/fig10.06.ps}\end{figure}">|; 

$key = q/{displaymath}S(Z)={{aZ+b}over{bZ+a}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="41" BORDER="0"
 SRC="|."$dir".q|img953.png"
 ALT="\begin{displaymath}
S(Z) =
{{
aZ + b
} \over {
bZ + a
}}
\end{displaymath}">|; 

$key = q/{omega_b}slashomega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img588.png"
 ALT="${\omega_b}/\omega$">|; 

$key = q/Y[k];MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="33" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1062.png"
 ALT="$Y[k]$">|; 

$key = q/{displaymath}{|{y_1}|}^2+{|{y_2}|}^2={|{x_1}|}^2+{|{x_2}|}^2{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="183" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img754.png"
 ALT="\begin{displaymath}
{\vert{y_1}\vert}^2 + {\vert{y_2}\vert}^2 = {\vert{x_1}\vert}^2 + {\vert{x_2}\vert}^2
\end{displaymath}">|; 

$key = q/{displaymath}ldots,{Z^0},{Z^1},{Z^2},ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img657.png"
 ALT="\begin{displaymath}
\ldots, {Z^0}, {Z^1}, {Z^2}, \ldots
\end{displaymath}">|; 

$key = q/f(t);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img307.png"
 ALT="$f(t)$">|; 

$key = q/1slash(2f);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img841.png"
 ALT="$1/(2f)$">|; 

$key = q/T';MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="19" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1211.png"
 ALT="$T'$">|; 

$key = q/fbox{{mathrm{trigger}{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="40" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img354.png"
 ALT="\fbox{ $\mathrm{trigger}$}">|; 

$key = q/fbox{{mathrm{clip}sim{};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="41" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img492.png"
 ALT="\fbox{$\mathrm{clip}\sim$}">|; 

$key = q/pi+omega;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img301.png"
 ALT="$\pi + \omega$">|; 

$key = q/c_2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img618.png"
 ALT="$c_2$">|; 

$key = q/p+q=1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="67" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img590.png"
 ALT="$p + q = 1$">|; 

$key = q/d=1.5;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img782.png"
 ALT="$d=1.5$">|; 

$key = q/{figure}{psfig{file=figsslashfig07.07.ps}{{{{figure};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="125" HEIGHT="221" BORDER="0"
 SRC="|."$dir".q|img708.png"
 ALT="\begin{figure}\psfig{file=figs/fig07.07.ps}\end{figure}">|; 

$key = q/1slashM;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1344.png"
 ALT="$1/M$">|; 

$key = q/omegan;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img575.png"
 ALT="$\omega n$">|; 

$key = q/n^2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1299.png"
 ALT="$n^2$">|; 

$key = q/{L_1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img1281.png"
 ALT="${L_1}$">|; 

$key = q/Rslash10;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="39" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img817.png"
 ALT="$R/10$">|; 

$key = q/Phi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1119.png"
 ALT="$\Phi$">|; 

$key = q/N=512;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1226.png"
 ALT="$N=512$">|; 

$key = q/fbox{texttt{vd~}};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="39" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img825.png"
 ALT="\fbox{ \texttt{vd\&nbsp;}}">|; 

$key = q/{displaymath}g[m,k]={{|T[m,k]|}over{|S[m,k]|}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img1175.png"
 ALT="\begin{displaymath}
g[m, k] = {{\vert T[m, k]\vert}\over{\vert S[m, k]\vert}}
\end{displaymath}">|; 

$key = q/{displaymath}{{sin(komegan)}over{kpi}}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="61" HEIGHT="40" BORDER="0"
 SRC="|."$dir".q|img1324.png"
 ALT="\begin{displaymath}
{{\sin ( k \omega n)} \over {k \pi}}
\end{displaymath}">|; 

$key = q/{a_0}slash100;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="50" HEIGHT="32" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="${a_0}/100$">|; 

$key = q/i=sqrt{-1};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="36" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img625.png"
 ALT="$i=\sqrt{-1}$">|; 

$key = q/{displaymath}{c_0}=2{a_0},{c_1}=2{a_2},{c_2}=2{a_4},ldots{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img240.png"
 ALT="\begin{displaymath}
{c_0} = 2{a_0}, {c_1} = 2{a_2}, {c_2} = 2{a_4}, \ldots
\end{displaymath}">|; 

1;