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miller-book/images.pl

9656 lines
300 KiB

# 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/;
$cached_env_img{$