You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
11113 lines
234 KiB
11113 lines
234 KiB
\batchmode
|
|
\input{psfig.sty}
|
|
\documentclass{book}
|
|
\RequirePackage{ifthen}
|
|
|
|
|
|
\usepackage{html}
|
|
\usepackage{makeidx}
|
|
\makeindex
|
|
|
|
|
|
|
|
|
|
\usepackage[dvips]{color}
|
|
|
|
|
|
\pagecolor[gray]{.7}
|
|
|
|
\usepackage[latin1]{inputenc}
|
|
|
|
|
|
|
|
\makeatletter
|
|
\AtBeginDocument{\makeatletter
|
|
\input /home/msp/papers/book/book.aux
|
|
\makeatother
|
|
}
|
|
|
|
\makeatletter
|
|
\count@=\the\catcode`\_ \catcode`\_=8
|
|
\newenvironment{tex2html_wrap}{}{}%
|
|
\catcode`\<=12\catcode`\_=\count@
|
|
\newcommand{\providedcommand}[1]{\expandafter\providecommand\csname #1\endcsname}%
|
|
\newcommand{\renewedcommand}[1]{\expandafter\providecommand\csname #1\endcsname{}%
|
|
\expandafter\renewcommand\csname #1\endcsname}%
|
|
\newcommand{\newedenvironment}[1]{\newenvironment{#1}{}{}\renewenvironment{#1}}%
|
|
\let\newedcommand\renewedcommand
|
|
\let\renewedenvironment\newedenvironment
|
|
\makeatother
|
|
\let\mathon=$
|
|
\let\mathoff=$
|
|
\ifx\AtBeginDocument\undefined \newcommand{\AtBeginDocument}[1]{}\fi
|
|
\newbox\sizebox
|
|
\setlength{\hoffset}{0pt}\setlength{\voffset}{0pt}
|
|
\addtolength{\textheight}{\footskip}\setlength{\footskip}{0pt}
|
|
\addtolength{\textheight}{\topmargin}\setlength{\topmargin}{0pt}
|
|
\addtolength{\textheight}{\headheight}\setlength{\headheight}{0pt}
|
|
\addtolength{\textheight}{\headsep}\setlength{\headsep}{0pt}
|
|
\setlength{\textwidth}{349pt}
|
|
\newwrite\lthtmlwrite
|
|
\makeatletter
|
|
\let\realnormalsize=\normalsize
|
|
\global\topskip=2sp
|
|
\def\preveqno{}\let\real@float=\@float \let\realend@float=\end@float
|
|
\def\@float{\let\@savefreelist\@freelist\real@float}
|
|
\def\liih@math{\ifmmode$\else\bad@math\fi}
|
|
\def\end@float{\realend@float\global\let\@freelist\@savefreelist}
|
|
\let\real@dbflt=\@dbflt \let\end@dblfloat=\end@float
|
|
\let\@largefloatcheck=\relax
|
|
\let\if@boxedmulticols=\iftrue
|
|
\def\@dbflt{\let\@savefreelist\@freelist\real@dbflt}
|
|
\def\adjustnormalsize{\def\normalsize{\mathsurround=0pt \realnormalsize
|
|
\parindent=0pt\abovedisplayskip=0pt\belowdisplayskip=0pt}%
|
|
\def\phantompar{\csname par\endcsname}\normalsize}%
|
|
\def\lthtmltypeout#1{{\let\protect\string \immediate\write\lthtmlwrite{#1}}}%
|
|
\newcommand\lthtmlhboxmathA{\adjustnormalsize\setbox\sizebox=\hbox\bgroup\kern.05em }%
|
|
\newcommand\lthtmlhboxmathB{\adjustnormalsize\setbox\sizebox=\hbox to\hsize\bgroup\hfill }%
|
|
\newcommand\lthtmlvboxmathA{\adjustnormalsize\setbox\sizebox=\vbox\bgroup %
|
|
\let\ifinner=\iffalse \let\)\liih@math }%
|
|
\newcommand\lthtmlboxmathZ{\@next\next\@currlist{}{\def\next{\voidb@x}}%
|
|
\expandafter\box\next\egroup}%
|
|
\newcommand\lthtmlmathtype[1]{\gdef\lthtmlmathenv{#1}}%
|
|
\newcommand\lthtmllogmath{\dimen0\ht\sizebox \advance\dimen0\dp\sizebox
|
|
\ifdim\dimen0>.95\vsize
|
|
\lthtmltypeout{%
|
|
*** image for \lthtmlmathenv\space is too tall at \the\dimen0, reducing to .95 vsize ***}%
|
|
\ht\sizebox.95\vsize \dp\sizebox\z@ \fi
|
|
\lthtmltypeout{l2hSize %
|
|
:\lthtmlmathenv:\the\ht\sizebox::\the\dp\sizebox::\the\wd\sizebox.\preveqno}}%
|
|
\newcommand\lthtmlfigureA[1]{\let\@savefreelist\@freelist
|
|
\lthtmlmathtype{#1}\lthtmlvboxmathA}%
|
|
\newcommand\lthtmlpictureA{\bgroup\catcode`\_=8 \lthtmlpictureB}%
|
|
\newcommand\lthtmlpictureB[1]{\lthtmlmathtype{#1}\egroup
|
|
\let\@savefreelist\@freelist \lthtmlhboxmathB}%
|
|
\newcommand\lthtmlpictureZ[1]{\hfill\lthtmlfigureZ}%
|
|
\newcommand\lthtmlfigureZ{\lthtmlboxmathZ\lthtmllogmath\copy\sizebox
|
|
\global\let\@freelist\@savefreelist}%
|
|
\newcommand\lthtmldisplayA{\bgroup\catcode`\_=8 \lthtmldisplayAi}%
|
|
\newcommand\lthtmldisplayAi[1]{\lthtmlmathtype{#1}\egroup\lthtmlvboxmathA}%
|
|
\newcommand\lthtmldisplayB[1]{\edef\preveqno{(\theequation)}%
|
|
\lthtmldisplayA{#1}\let\@eqnnum\relax}%
|
|
\newcommand\lthtmldisplayZ{\lthtmlboxmathZ\lthtmllogmath\lthtmlsetmath}%
|
|
\newcommand\lthtmlinlinemathA{\bgroup\catcode`\_=8 \lthtmlinlinemathB}
|
|
\newcommand\lthtmlinlinemathB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA
|
|
\vrule height1.5ex width0pt }%
|
|
\newcommand\lthtmlinlineA{\bgroup\catcode`\_=8 \lthtmlinlineB}%
|
|
\newcommand\lthtmlinlineB[1]{\lthtmlmathtype{#1}\egroup\lthtmlhboxmathA}%
|
|
\newcommand\lthtmlinlineZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
|
|
\expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetinline}
|
|
\newcommand\lthtmlinlinemathZ{\egroup\expandafter\ifdim\dp\sizebox>0pt %
|
|
\expandafter\centerinlinemath\fi\lthtmllogmath\lthtmlsetmath}
|
|
\newcommand\lthtmlindisplaymathZ{\egroup %
|
|
\centerinlinemath\lthtmllogmath\lthtmlsetmath}
|
|
\def\lthtmlsetinline{\hbox{\vrule width.1em \vtop{\vbox{%
|
|
\kern.1em\copy\sizebox}\ifdim\dp\sizebox>0pt\kern.1em\else\kern.3pt\fi
|
|
\ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
|
|
\def\lthtmlsetmath{\hbox{\vrule width.1em\kern-.05em\vtop{\vbox{%
|
|
\kern.1em\kern0.8 pt\hbox{\hglue.17em\copy\sizebox\hglue0.8 pt}}\kern.3pt%
|
|
\ifdim\dp\sizebox>0pt\kern.1em\fi \kern0.8 pt%
|
|
\ifdim\hsize>\wd\sizebox \hrule depth1pt\fi}}}
|
|
\def\centerinlinemath{%
|
|
\dimen1=\ifdim\ht\sizebox<\dp\sizebox \dp\sizebox\else\ht\sizebox\fi
|
|
\advance\dimen1by.5pt \vrule width0pt height\dimen1 depth\dimen1
|
|
\dp\sizebox=\dimen1\ht\sizebox=\dimen1\relax}
|
|
|
|
\def\lthtmlcheckvsize{\ifdim\ht\sizebox<\vsize
|
|
\ifdim\wd\sizebox<\hsize\expandafter\hfill\fi \expandafter\vfill
|
|
\else\expandafter\vss\fi}%
|
|
\providecommand{\selectlanguage}[1]{}%
|
|
\makeatletter \tracingstats = 1
|
|
|
|
|
|
\begin{document}
|
|
\pagestyle{empty}\thispagestyle{empty}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength hsize=\the\hsize}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength vsize=\the\vsize}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength hoffset=\the\hoffset}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength voffset=\the\voffset}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength topmargin=\the\topmargin}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength topskip=\the\topskip}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength headheight=\the\headheight}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength headsep=\the\headsep}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength parskip=\the\parskip}\lthtmltypeout{}%
|
|
\lthtmltypeout{latex2htmlLength oddsidemargin=\the\oddsidemargin}\lthtmltypeout{}%
|
|
\makeatletter
|
|
\if@twoside\lthtmltypeout{latex2htmlLength evensidemargin=\the\evensidemargin}%
|
|
\else\lthtmltypeout{latex2htmlLength evensidemargin=\the\oddsidemargin}\fi%
|
|
\lthtmltypeout{}%
|
|
\makeatother
|
|
\setcounter{page}{1}
|
|
\onecolumn
|
|
|
|
% !!! IMAGES START HERE !!!
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19209}%
|
|
$\sqrt 2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19212}%
|
|
$y[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19215}%
|
|
$N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19218}%
|
|
$a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19221}%
|
|
$\pi /2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19223}%
|
|
$3\pi /2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19227}%
|
|
$\alpha $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19229}%
|
|
$\beta $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19231}%
|
|
$\alpha > \beta > 0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19233}%
|
|
$\beta > \alpha $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19235}%
|
|
$f=0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19237}%
|
|
$\alpha =\beta $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19239}%
|
|
$\alpha =0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19248}%
|
|
$f()$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19251}%
|
|
$f(x) = {x^2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19254}%
|
|
$2\pi $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19257}%
|
|
$W(\phi )=(1+\mathop {\mathgroup \symoperators cos}\nolimits (\phi ))/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19259}%
|
|
$a=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19261}%
|
|
$a=2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19269}%
|
|
$Z$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19273}%
|
|
$b$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19280}%
|
|
$|Z|=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19282}%
|
|
$A$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19289}%
|
|
$Z^-d$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19291}%
|
|
$H$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19295}%
|
|
$d/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19302}%
|
|
$\omega $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19305}%
|
|
$d$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19307}%
|
|
$g$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19311}%
|
|
$|H|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19313}%
|
|
$W$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19323}%
|
|
$g = 0.8$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19325}%
|
|
$1/(1-g)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19329}%
|
|
$\theta = \pi /4$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19331}%
|
|
$a = \mathop {\mathgroup \symoperators cos}\nolimits (\theta ) = \mathop {\mathgroup \symoperators sin}\nolimits (\theta ) = \sqrt {1/2} \approx 0.7071$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19335}%
|
|
$R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19338}%
|
|
$t_1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19340}%
|
|
$t_2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19342}%
|
|
$t_3$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19347}%
|
|
$D$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19350}%
|
|
$\pi $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19353}%
|
|
$Q$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19355}%
|
|
$Q=-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19367}%
|
|
$r=|Q|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19371}%
|
|
$r=0.5$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19374}%
|
|
$\beta = \pi /4$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19376}%
|
|
$\beta =\pi $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19378}%
|
|
$\beta =3\pi /10$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19380}%
|
|
$\beta =2\pi /10$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19382}%
|
|
$\beta =0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19389}%
|
|
$R(Z) = -{Z^2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19395}%
|
|
$\pi /4$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19398}%
|
|
$P=0.8$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19400}%
|
|
$P=0.9$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19402}%
|
|
$|P|=0.9$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19404}%
|
|
$2\pi /10$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19410}%
|
|
$p$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19413}%
|
|
$k$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19421}%
|
|
$2\omega $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19423}%
|
|
$1.5\omega $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19428}%
|
|
$\alpha =1.5\omega =3\pi /N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19437}%
|
|
$D_N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19439}%
|
|
$N=100$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19443}%
|
|
$S[m, k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19446}%
|
|
$\@mathrm {fft}\sim $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19449}%
|
|
$(M, c)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19451}%
|
|
$(0, 8)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19453}%
|
|
$(N/2, -8)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19458}%
|
|
$(M, 1)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19460}%
|
|
$(N-M, -1)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19464}%
|
|
$M/N=0.03$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19466}%
|
|
$1/k$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline19468}%
|
|
$1/{k^2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
|
|
%
|
|
\providecommand{\patchAA}{A01.sinewave.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchAB}{A02.amplitude.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchAC}{A03.line.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchACbis}{A04.line2.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchAD}{A05.output.subpatch.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchAE}{A06.frequency.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchAG}{A07.fusion.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchAH}{A08.beating.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchAI}{A09.frequency.mod.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBA}{B01.wavetables.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBB}{B02.wavetable.FM.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBC}{B03.tabread4.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBD}{B04.sampler.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBE}{B05.sampler.loop.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBF}{B06.sampler.loop.smooth.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBG}{B07.sampler.scratch.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBH}{B08.sampler.nodoppler.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBI}{B09.sampler.transpose.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBJ}{B10.sampler.overlap.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchBK}{B11.sampler.rockafella.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCA}{C01.nyquist.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCB}{C02.sawtooth-foldover.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCC}{C03.zipper.noise.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCD}{C04.control.to.signal.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCE}{C05.sampler.oneshot.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCF}{C06.signal.to.control.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCG}{C07.envelope.follower.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCH}{C08.analog.sequencer.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCI}{C09.sample.hold.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchCJ}{C10.monophonic.synth.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDA}{D01.envelope.gen.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDB}{D02.adsr.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDC}{D03.envelope.dB.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDD}{D04.envelope.quartic.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDE}{D05.envelope.pitch.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDF}{D06.envelope.portamento.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDG}{D07.additive.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDH}{D08.table.spectrum.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDI}{D09.shepard.tone.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDJ}{D10.sampler.notes.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchDK}{D11.sampler.poly.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEA}{E01.spectrum.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEB}{E02.ring.modulation.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEC}{E03.octave.divider.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchED}{E04.difference.tone.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEE}{E05.chebychev.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEF}{E06.exponential.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEG}{E07.evenodd.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEH}{E08.phase.mod.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEI}{E09.FM.spectrum.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchEJ}{E10.complex.FM.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchFA}{F01.pulse.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchFE}{F05.ring.modulation.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchFF}{F06.packets.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchFH}{F08.two.cosines.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchFI}{F09.declickit.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchFL}{F12.paf.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchFM}{F13.paf.control.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchFN}{F14.wave.packet.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGA}{G01.delay.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGB}{G02.delay.loop.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGC}{G03.delay.variable.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGD}{G04.control.blocksize.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGE}{G05.execution.order.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGF}{G06.octave.doubler.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGG}{G07.shaker.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGH}{G08.reverb.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchGI}{G09.pitchshift.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHA}{H01.low-pass.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHB}{H02.high-pass.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHC}{H03.band-pass.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHD}{H04.filter.sweep.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHE}{H05.filter.floyd.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHF}{H06.envelope.follower.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHG}{H07.measure.spectrum.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHH}{H08.heterodyning.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHI}{H09.ssb.modulation.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHJ}{H10.measurement.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHK}{H11.shelving.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHL}{H12.peaking.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHM}{H13.butterworth.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHN}{H14.all.pass.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchHO}{H15.phaser.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchIA}{I01.Fourier.analysis.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchIB}{I02.Hann.window.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchIC}{I03.resynthesis.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchID}{I04.noisegate.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchIE}{I05.compressor.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchIF}{I06.timbre.stamp.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchIG}{I07.phase.vocoder.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchIH}{I08.pvoc.reverb.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchII}{I09.sheep.from.goats.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchIJ}{I10.phase.bash.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJA}{J01.even.odd.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJB}{J02.trapezoids.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJC}{J03.pulse.width.mod.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJD}{J04.corners.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJE}{J05.triangle.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJF}{J06.enveloping.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJG}{J07.oversampling.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJH}{J08.classicsynth.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\patchJI}{J09.bandlimited.pd}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdplus}{\texttt{+}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pddbtorms}{\texttt{dbtorms}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pddelay}{\texttt{delay}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pddel}{\texttt{del}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pddiv}{\texttt{div}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdexpr}{\texttt{expr}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdftom}{\texttt{ftom}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdf}{\texttt{f}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdfloat}{\texttt{float}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdinlet}{\texttt{inlet}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdline}{\texttt{line}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdmakefilename}{\texttt{makefilename}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdmakenote}{\texttt{makenote}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdmetro}{\texttt{metro}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdmod}{\texttt{pdmod}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdmoses}{\texttt{moses}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdmtof}{\texttt{mtof}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdnotein}{\texttt{notein}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdoutlet}{\texttt{outlet}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdpack}{\texttt{pack}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdpipe}{\texttt{pipe}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdpoly}{\texttt{poly}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdr}{\texttt{r}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdreceive}{\texttt{receive}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdroute}{\texttt{route}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pds}{\texttt{s}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdsend}{\texttt{send}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdselect}{\texttt{select}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdstripnote}{\texttt{stripnote}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtabreadfour}{\texttt{tabread4}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtabread}{\texttt{tabread}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtabwrite}{\texttt{tabwrite}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtrigger}{\texttt{trigger}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdunpack}{\texttt{pdunpack}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pduntil}{\texttt{until}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtimestilde}{\texttt{*\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdplustilde}{\texttt{+\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdbangtilde}{\texttt{bang\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdbiquadtilde}{\texttt{biquad\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdblocktilde}{\texttt{block\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdbptilde}{\texttt{bp\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdcatchtilde}{\texttt{catch\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdcliptilde}{\texttt{clip\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdcostilde}{\texttt{cos\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdcpoletilde}{\texttt{cpole\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdczerorevtilde}{\texttt{czero\_rev\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdczerotilde}{\texttt{czero\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pddactilde}{\texttt{dac\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pddbtormstilde}{\texttt{dbtorms\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pddelreadtilde}{\texttt{delread\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pddelwritetilde}{\texttt{delwrite\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdffttilde}{\texttt{fft\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdfiddletilde}{\texttt{fiddle\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdhiptilde}{\texttt{hip\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdiffttilde}{\texttt{ifft\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdinlettilde}{\texttt{inlet\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdlinetilde}{\texttt{line\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdloptilde}{\texttt{lop\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdlrshifttilde}{\texttt{lrshift\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdnoisetilde}{\texttt{noise\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdosctilde}{\texttt{osc\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdoutlettilde}{\texttt{outlet\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdphasortilde}{\texttt{phasor\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdreceivetilde}{\texttt{receive\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdrffttilde}{\texttt{rfft\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdriffttilde}{\texttt{rifft\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdrpoletilde}{\texttt{rpole\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdrzerorevtilde}{\texttt{rzero\_rev\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdrzerotilde}{\texttt{rzero\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdsampholdtilde}{\texttt{samphold\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdsendtilde}{\texttt{send\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdsqrttilde}{\texttt{sqrt\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdswitchtilde}{\texttt{switch\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtaboscfourtilde}{\texttt{tabosc4\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtabreadfourtilde}{\texttt{tabread4\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtabreadtilde}{\texttt{tabread\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtabreceivetilde}{\texttt{tabreceive\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtabsendtilde}{\texttt{tabsend\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdtabwritetilde}{\texttt{tabwrite\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdthrowtilde}{\texttt{throw\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdvcftilde}{\texttt{vcf\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdvdtilde}{\texttt{vd\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdvlinetilde}{\texttt{vline\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdwraptilde}{\texttt{wrap\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdoutputtilde}{\texttt{output\~}}%
|
|
|
|
|
|
%
|
|
\providecommand{\pdobject}[1]{\texttt{#1}}%
|
|
|
|
|
|
%
|
|
\providecommand{\refchapterwavetab}{2}%
|
|
|
|
|
|
%
|
|
\providecommand{\refchaptermod}{5}%
|
|
|
|
|
|
%
|
|
\providecommand{\refchapterpaf}{6}%
|
|
|
|
|
|
%
|
|
\providecommand{\refchapterdel}{7}%
|
|
|
|
|
|
%
|
|
\providecommand{\refchapterfft}{9}%
|
|
|
|
\stepcounter{chapter}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1490}%
|
|
\begin{displaymath}
|
|
..., x[n-1], x[n], x[n+1], ...
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1530}%
|
|
$n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1491}%
|
|
\begin{displaymath}
|
|
x[n] = a \cos (\omega n + \phi )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1536}%
|
|
$\phi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1540}%
|
|
$\omega n + \phi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1542}%
|
|
$n=0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1546}%
|
|
$x[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1026}%
|
|
\begin{figure}\psfig{file=figs/fig01.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1550}%
|
|
$t$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1554}%
|
|
$Rt = n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1556}%
|
|
$t = n/R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1492}%
|
|
\begin{displaymath}
|
|
f = {{\omega R} \over {2 \pi}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1566}%
|
|
$M$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1493}%
|
|
\begin{displaymath}
|
|
x[M], x[M+1], \ldots, x[M+N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1494}%
|
|
\begin{displaymath}
|
|
{A_{\mathrm{peak}}} \{x[n]\} = \max | x[n] | ,
|
|
\hspace{0.3in}n = M, \ldots, M+N-1
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1495}%
|
|
\begin{displaymath}
|
|
{A_{\mathrm{RMS}}} \{x[n]\} = \sqrt{P\{x[n]\}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1572}%
|
|
$P\{x[n]\}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1496}%
|
|
\begin{displaymath}
|
|
{P\{x[n]\}} = {1 \over N} \left (
|
|
{{|x[M]|} ^2} + \cdots + {{|x[M+N-1]|} ^2}
|
|
\right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1576}%
|
|
$1 / {\sqrt N}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1057}%
|
|
\begin{figure}\psfig{file=figs/fig01.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1582}%
|
|
$a / {\sqrt 2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1497}%
|
|
\begin{displaymath}
|
|
d = 20 \cdot {{{\log}_{10}} ( {a / {a_0}} )}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1588}%
|
|
$a_0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1590}%
|
|
$\sqrt {10}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1592}%
|
|
$1/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1073}%
|
|
\begin{figure}\psfig{file=figs/fig01.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1598}%
|
|
${a_0}/10$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1600}%
|
|
${a_0}/100$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1602}%
|
|
$-\infty$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1498}%
|
|
\begin{displaymath}
|
|
{a_0} = {10^{-5}} = 0.00001
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1088}%
|
|
\begin{figure}\psfig{file=figs/fig01.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1608}%
|
|
$y \ge
|
|
0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1610}%
|
|
$y$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1612}%
|
|
$y \cdot
|
|
x[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1622}%
|
|
$y[n] \cdot x[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1626}%
|
|
$M+N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1638}%
|
|
${2 ^ {1/{12}}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1640}%
|
|
$m$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1642}%
|
|
$f$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1499}%
|
|
\begin{displaymath}
|
|
m = 69 + 12 \cdot {\log _ 2} (f/440)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1500}%
|
|
\begin{displaymath}
|
|
f = 440 \cdot {{2} ^ {(m - 69) / 12}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1644}%
|
|
$m=60$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1646}%
|
|
$f=261.626$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1121}%
|
|
\begin{figure}\psfig{file=figs/fig01.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1127}%
|
|
\begin{figure}\psfig{file=figs/fig01.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1501}%
|
|
\begin{displaymath}
|
|
y[n] = a + (b - a) {{n-M} \over N}, \hspace{0.1in} M \le n \le M+N-1.
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1674}%
|
|
$a=b$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1146}%
|
|
\begin{figure}\psfig{file=figs/fig01.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1680}%
|
|
$k \cdot x[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1682}%
|
|
$k \ge 0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1684}%
|
|
$kA$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1686}%
|
|
$k^2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1502}%
|
|
\begin{displaymath}
|
|
{A_{\mathrm{peak}}} \{x[n]\} +
|
|
{A_{\mathrm{peak}}} \{y[n]\} \ge
|
|
{A_{\mathrm{peak}}} \{x[n]+y[n]\}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1503}%
|
|
\begin{displaymath}
|
|
{A_{\mathrm{RMS}}} \{x[n]\} +
|
|
{A_{\mathrm{RMS}}} \{y[n]\} \ge
|
|
{A_{\mathrm{RMS}}} \{x[n]+y[n]\}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1694}%
|
|
$N+M-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1504}%
|
|
\begin{displaymath}
|
|
P \{x[n] + y[n]\} = P \{x[n]\} + P \{y[n]\}
|
|
+ 2 \cdot {\mathrm{COV}} \{ x[n] , y[n] \}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1505}%
|
|
\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}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1506}%
|
|
\begin{displaymath}
|
|
P \{x[n] + y[n]\} = P \{x[n]\} + P \{y[n]\} , \hspace{0.1in}
|
|
\mathrm{whenever}
|
|
\ {\mathrm{COV}} \{ x[n] , y[n] \} = 0
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1507}%
|
|
\begin{displaymath}
|
|
{{\left ( {A_{\mathrm{RMS}}} \{x[n]+y[n]\} \right ) } ^ 2} =
|
|
{{\left ( {A_{\mathrm{RMS}}} \{x[n]\} \right ) } ^ 2} +
|
|
{{\left ( {A_{\mathrm{RMS}}} \{y[n]\} \right ) } ^ 2} .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1698}%
|
|
${\sqrt 2} a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1700}%
|
|
$2a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1704}%
|
|
$\tau$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1508}%
|
|
\begin{displaymath}
|
|
x[n + \tau] = x[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1708}%
|
|
$2 \tau$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1716}%
|
|
$2 \pi / \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1720}%
|
|
$2 \pi k/ \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath1509}%
|
|
\begin{displaymath}
|
|
x[n] = {a_0} +
|
|
{a_1} \cos \left ( \omega n + {\phi_1} \right ) +
|
|
{a_2} \cos \left ( 2 \omega n + {\phi_2} \right ) + \cdots +
|
|
{a_p} \cos \left ( p \omega n + {\phi_p} \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1730}%
|
|
$\omega, 2 \omega, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1194}%
|
|
\begin{figure}\psfig{file=figs/fig01.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1200}%
|
|
\begin{figure}\psfig{file=figs/fig01.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1236}%
|
|
\begin{figure}\psfig{file=figs/fig01.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1254}%
|
|
\begin{figure}\psfig{file=figs/fig01.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1994}%
|
|
\fbox{ $ \mathrm{osc}\sim $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2000}%
|
|
\fbox{ $*\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2006}%
|
|
\fbox{ $ \mathrm{dac}\sim $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1271}%
|
|
\begin{figure}\psfig{file=figs/fig01.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2026}%
|
|
\fbox{ $ \mathrm{dbtorms} $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2028}%
|
|
\fbox{ $ \mathrm{dbtorms}\sim $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2040}%
|
|
\fbox{ $ \mathrm{line}\sim $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1294}%
|
|
\begin{figure}\psfig{file=figs/fig01.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2070}%
|
|
\fbox{ $ \mathrm{mtof} $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2072}%
|
|
\fbox{ $ \mathrm{ftom} $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2080}%
|
|
\fbox{ $ \mathrm{receive} $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2082}%
|
|
\fbox{ $ \mathrm{r} $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2090}%
|
|
\fbox{ $\mathrm{send}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2092}%
|
|
\fbox{ $\mathrm{s}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1320}%
|
|
\begin{figure}\psfig{file=figs/fig01.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure1328}%
|
|
\begin{figure}\psfig{file=figs/fig01.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1776}%
|
|
$\phi=0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1778}%
|
|
$\omega = \pi/10$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1780}%
|
|
$n=10$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline1782}%
|
|
$x[n], n = 0, ..., N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2726}%
|
|
$n = 0, ..., N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2734}%
|
|
$z[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2656}%
|
|
\begin{displaymath}
|
|
z[n] = x[y[n]]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2154}%
|
|
\begin{figure}\psfig{file=figs/fig02.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2740}%
|
|
$0, ..., N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2746}%
|
|
$N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2657}%
|
|
\begin{displaymath}
|
|
z[n] = \left \{ {
|
|
\begin{array}{ll}
|
|
x[ \lfloor y[n] \rfloor ] & \mbox{if $0 \le y[n] < N-1$} \\
|
|
x[0] & \mbox{if $y[n] < 0$} \\
|
|
x[N-1] & \mbox{if $y[n] \ge N-1$} \\
|
|
\end{array}
|
|
} \right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2754}%
|
|
$\lfloor y[n] \rfloor$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2758}%
|
|
$y[0]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2760}%
|
|
$z[0]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2762}%
|
|
$y[1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2764}%
|
|
$z[1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2768}%
|
|
$0 \le y[n] < N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2774}%
|
|
$0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2776}%
|
|
$40$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2778}%
|
|
$R/20$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2174}%
|
|
\begin{figure}\psfig{file=figs/fig02.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2188}%
|
|
\begin{figure}\psfig{file=figs/fig02.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2802}%
|
|
$2\pi/N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2804}%
|
|
$0 \le x[n] \le 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2806}%
|
|
$x[n] = 0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2808}%
|
|
$x[n] = 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2658}%
|
|
\begin{displaymath}
|
|
(1 - x[n])y[n] + x[n]z[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2659}%
|
|
\begin{displaymath}
|
|
y[n] + x[n](z[n]-y[n])
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2196}%
|
|
\begin{figure}\psfig{file=figs/fig02.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2826}%
|
|
$N/M$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2828}%
|
|
$N f / R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2834}%
|
|
$t=3/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2836}%
|
|
$h$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2660}%
|
|
\begin{displaymath}
|
|
t = {N / M} = {{N f} / R}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2661}%
|
|
\begin{displaymath}
|
|
h = 12 \, {\log _ 2} \left ( {N \over M} \right ) =
|
|
12 \, {\log _ 2} \left ( {N f \over R} \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2662}%
|
|
\begin{displaymath}
|
|
f = {{2^{h/12} R} \over N}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2663}%
|
|
\begin{displaymath}
|
|
N = {{2^{h/12} R} \over f}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2844}%
|
|
$y[t]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2664}%
|
|
\begin{displaymath}
|
|
t[n] = \left | y[n] - y[n-1] \right |
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2665}%
|
|
\begin{displaymath}
|
|
h[n] = 12 {{\log_2} \left | y[n] - y[n-1] \right |}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2850}%
|
|
$|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2852}%
|
|
$y[n] = n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2854}%
|
|
$z[n] = x[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2666}%
|
|
\begin{displaymath}
|
|
y[n]-y[n-1] = 1
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2856}%
|
|
$y[n] = 2n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2667}%
|
|
\begin{displaymath}
|
|
y[n]-y[n-1] = 2
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2872}%
|
|
$s$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2874}%
|
|
$t = fs/R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2880}%
|
|
$l$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2894}%
|
|
$l+s$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2898}%
|
|
$-1/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2904}%
|
|
$-s/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2906}%
|
|
$s/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2910}%
|
|
$l-s/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2912}%
|
|
$l+s/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2230}%
|
|
\begin{figure}\psfig{file=figs/fig02.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2241}%
|
|
\begin{figure}\psfig{file=figs/fig02.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2247}%
|
|
\begin{figure}\psfig{file=figs/fig02.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2254}%
|
|
\begin{figure}\psfig{file=figs/fig02.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2269}%
|
|
\begin{figure}\psfig{file=figs/fig02.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2668}%
|
|
\begin{displaymath}
|
|
{x_{100}}[n] = {a_0} +
|
|
{a_1} \cos \left ( \omega n + {\phi_1} \right ) +
|
|
{a_2} \cos \left ( 2 \omega n + {\phi_2} \right ) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2934}%
|
|
$\pi/10$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2936}%
|
|
${x_{50}}[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2669}%
|
|
\begin{displaymath}
|
|
{x_{100}}[2n] = {x_{50}}[n] + {x_{50}}[n+{\pi \over \omega}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2940}%
|
|
$\pi / \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2670}%
|
|
\begin{displaymath}
|
|
{x_{50}}[n] = {b_0} +
|
|
{b_1} \cos \left ( \omega n + {\theta_1} \right ) +
|
|
{b_2} \cos \left ( 2 \omega n + {\theta_2} \right ) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2671}%
|
|
\begin{displaymath}
|
|
{a_0} +
|
|
{a_1} \cos \left ( 2 \omega n + {\phi_1} \right ) +
|
|
{a_2} \cos \left ( 4 \omega n + {\phi_2} \right ) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2672}%
|
|
\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}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2673}%
|
|
\begin{displaymath}
|
|
+
|
|
{b_0} +
|
|
{b_1} \cos \left ( \omega n + \pi + {\theta_1} \right ) +
|
|
{b_2} \cos \left ( 2 \omega n + 2 \pi + {\theta_2} \right ) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2674}%
|
|
\begin{displaymath}
|
|
= 2 {b_0} +
|
|
2 {b_2} \cos \left ( 2 \omega n + {\theta_2} \right ) +
|
|
2 {b_4} \cos \left ( 4 \omega n + {\theta_4} \right ) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2675}%
|
|
\begin{displaymath}
|
|
{a_0} = 2{b_0}, \,\, {a_1} = 2{b_2}, \,\, {a_2} = 2{b_4}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2944}%
|
|
$x_{50}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2946}%
|
|
$x_{100}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2952}%
|
|
$x_{200}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2676}%
|
|
\begin{displaymath}
|
|
{x_{200}}[2n] = {x_{100}}[n] + {x_{100}}[n+{\pi \over \omega}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2956}%
|
|
$c_0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2958}%
|
|
$c_1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2960}%
|
|
$\ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2677}%
|
|
\begin{displaymath}
|
|
{c_0} = 2{a_0}, {c_1} = 2{a_2}, {c_2} = 2{a_4}, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2968}%
|
|
$1/f$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2340}%
|
|
\begin{figure}\psfig{file=figs/fig02.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2978}%
|
|
$x$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2980}%
|
|
${x_0}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2678}%
|
|
\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}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2982}%
|
|
$n+1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2988}%
|
|
$x_0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2992}%
|
|
$\lfloor x \rfloor$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2679}%
|
|
\begin{displaymath}
|
|
{y_{\mathrm{INT}}}(x) =
|
|
y[{x_0}] + (y[{x_0} + 1]- y[{x_0}]) \cdot (x - {x_0})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2680}%
|
|
\begin{displaymath}
|
|
{a_0} = y[{x_0}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2681}%
|
|
\begin{displaymath}
|
|
{a_1} = y[{x_0} + 1]- y[{x_0}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline2994}%
|
|
$n-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2372}%
|
|
\begin{figure}\psfig{file=figs/fig02.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2682}%
|
|
\begin{displaymath}
|
|
{y_{\mathrm{INT}}}(x) =
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2683}%
|
|
\begin{displaymath}
|
|
-f (f-1)(f-2)/6 \cdot y[{x_0}-1]
|
|
+ (f+1)(f-1)(f-2)/2 \cdot y[{x_0}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2684}%
|
|
\begin{displaymath}
|
|
- (f+1) f (f-2) / 2 \cdot y[{x_0}+1]
|
|
+ (f+1) f (f-1) / 6 \cdot y[{x_0}+2]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3000}%
|
|
$f = x - {x_0}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3006}%
|
|
$N + 1 - k$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3008}%
|
|
$k=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3020}%
|
|
$N-1/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3032}%
|
|
$N-2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3036}%
|
|
$1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3040}%
|
|
$N-3$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2685}%
|
|
\begin{displaymath}
|
|
x[n] = \cos(2 \pi n / N) ,\, n = 0, \ldots, N-1
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3044}%
|
|
$N+1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2686}%
|
|
\begin{displaymath}
|
|
x[n] = \cos(2 \pi n / N) ,\, n = 0, \ldots, N
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3052}%
|
|
$n=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3064}%
|
|
$N+2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3068}%
|
|
$2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3070}%
|
|
$N+3$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2687}%
|
|
\begin{displaymath}
|
|
x[n] = \cos(2 \pi (n-1) / N) ,\, n = 0, \ldots, N+2
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2398}%
|
|
\begin{figure}\psfig{file=figs/fig02.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3366}%
|
|
\fbox{ $ \mathrm{tabosc4}\sim $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3076}%
|
|
${2^m} + 3$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2410}%
|
|
\begin{figure}\psfig{file=figs/fig02.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3386}%
|
|
\fbox{ $\mathrm{tabread4}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3392}%
|
|
\fbox{ $\mathrm{tabwrite}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3402}%
|
|
\fbox{ $\mathrm{pack}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2428}%
|
|
\begin{figure}\psfig{file=figs/fig02.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3424}%
|
|
\fbox{ $\mathrm{hip}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2441}%
|
|
\begin{figure}\psfig{file=figs/fig02.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3444}%
|
|
\fbox{ $\mathrm{cos}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3100}%
|
|
$-\pi/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3458}%
|
|
\fbox{ $\mathrm{samphold}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure2464}%
|
|
\begin{figure}\psfig{file=figs/fig02.16.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3478}%
|
|
\fbox{ $\mathrm{loadbang}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3484}%
|
|
\fbox{ $\mathrm{expr}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3490}%
|
|
\fbox{$\mathrm{wrap}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3496}%
|
|
\fbox{ $\mathrm{send}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3498}%
|
|
\fbox{ $\mathrm{s}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3500}%
|
|
\fbox{ $\mathrm{receive}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3502}%
|
|
\fbox{ $\mathrm{r}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3140}%
|
|
$c$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2688}%
|
|
\begin{displaymath}
|
|
t = p + cf
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath2689}%
|
|
\begin{displaymath}
|
|
f = {{t - p} \over c} = {{{{2 ^ {h/12}}} - p} \over c}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3148}%
|
|
$1000$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3150}%
|
|
$R=44100$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3946}%
|
|
\begin{displaymath}
|
|
f(n) = 1 \, , \, \, \, \, \, n = \, \, \ldots, -1, 0, 1, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3972}%
|
|
$f(t)=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3984}%
|
|
$R/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline3992}%
|
|
$\pi + \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3947}%
|
|
\begin{displaymath}
|
|
\cos((\pi + \omega)n + \phi) = \cos((\pi + \omega)n + \phi - 2\pi n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3948}%
|
|
\begin{displaymath}
|
|
= \cos((\omega - \pi)n + \phi)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3949}%
|
|
\begin{displaymath}
|
|
= \cos((\pi - \omega)n - \phi)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4006}%
|
|
$\infty$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3562}%
|
|
\begin{figure}\psfig{file=figs/fig03.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4024}%
|
|
$f(t)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3950}%
|
|
\begin{displaymath}
|
|
f(t) = {1 \over 2} - {1 \over \pi}
|
|
{ \left (
|
|
\sin(\omega t) + {{\sin(2 \omega t)} \over 2} +
|
|
{{\sin(3 \omega t)} \over 3} + \cdots
|
|
\right ) }
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4030}%
|
|
$1/n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3582}%
|
|
\begin{figure}\psfig{file=figs/fig03.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4036}%
|
|
$B$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4038}%
|
|
$B=4$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4040}%
|
|
$0, 1, ... B-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3590}%
|
|
\begin{figure}\psfig{file=figs/fig03.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3951}%
|
|
\begin{displaymath}
|
|
\ldots , t[0], t[1], t[2], \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3952}%
|
|
\begin{displaymath}
|
|
\cdots \le t[0] \le t[1] \le t[2] \le \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3953}%
|
|
\begin{displaymath}
|
|
\ldots , \, (t[0], x[0]), \, (t[1], x[1]), \, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4048}%
|
|
$t[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3954}%
|
|
\begin{displaymath}
|
|
(2, 1), (4.75, 0), (7.5, 1), (10.25, 0), (13, 1), \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4054}%
|
|
$R/B$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3607}%
|
|
\begin{figure}\psfig{file=figs/fig03.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4058}%
|
|
$\lfloor t \rfloor$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4064}%
|
|
$(n+f, y)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4070}%
|
|
$0 \le f < 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3955}%
|
|
\begin{displaymath}
|
|
fx + (1-f)y,
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3956}%
|
|
\begin{displaymath}
|
|
0 \cdot x + 1 \cdot y = 1,
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath3957}%
|
|
\begin{displaymath}
|
|
0.75 \cdot x + 0.25 \cdot y = 0.75.
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3614}%
|
|
\begin{figure}\psfig{file=figs/fig03.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4084}%
|
|
$n-B$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3625}%
|
|
\begin{figure}\psfig{file=figs/fig03.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3640}%
|
|
\begin{figure}\psfig{file=figs/fig03.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4092}%
|
|
$3.999\ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3654}%
|
|
\begin{figure}\psfig{file=figs/fig03.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3663}%
|
|
\begin{figure}\psfig{file=figs/fig03.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3678}%
|
|
\begin{figure}\psfig{file=figs/fig03.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3688}%
|
|
\begin{figure}\psfig{file=figs/fig03.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3703}%
|
|
\begin{figure}\psfig{file=figs/fig03.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4370}%
|
|
\fbox{ $\mathrm{del}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4372}%
|
|
\fbox{ $\mathrm{delay}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4380}%
|
|
\fbox{ $\mathrm{pipe}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4390}%
|
|
\fbox{ $\mathrm{moses}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4396}%
|
|
\fbox{ $\mathrm{select}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4398}%
|
|
\fbox{ $\mathrm{sel}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3739}%
|
|
\begin{figure}\psfig{file=figs/fig03.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4428}%
|
|
\fbox{ $\mathrm{line}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4442}%
|
|
\fbox{ $\mathrm{vline}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3760}%
|
|
\begin{figure}\psfig{file=figs/fig03.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4476}%
|
|
\fbox{ $\mathrm{snapshot}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4484}%
|
|
\fbox{ $\mathrm{env}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3775}%
|
|
\begin{figure}\psfig{file=figs/fig03.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure3785}%
|
|
\begin{figure}\psfig{file=figs/fig03.16.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4514}%
|
|
\fbox{ $\mathrm{notein}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4520}%
|
|
\fbox{ $\mathrm{stripnote}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4526}%
|
|
\fbox{ $\mathrm{trigger}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline4528}%
|
|
\fbox{ $\mathrm{t}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4581}%
|
|
\begin{figure}\psfig{file=figs/fig04.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4591}%
|
|
\begin{figure}\psfig{file=figs/fig04.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5047}%
|
|
$10R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5051}%
|
|
$y[n] = n/(10R)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath5035}%
|
|
\begin{displaymath}
|
|
y[n] = {{ \left ( {{n} \over {N}} \right ) } ^ 4} ,
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath5036}%
|
|
\begin{displaymath}
|
|
{f_1} (x) = x \hspace{0.2in} \mathrm{(linear),}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath5037}%
|
|
\begin{displaymath}
|
|
\ \ \ \ \ \ \ %
|
|
{f_2} (x) = 10^{2(x-1)} \hspace{0.2in}\mathrm{(dB\ to\ linear),}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath5038}%
|
|
\begin{displaymath}
|
|
{f_3} (x) = {x^4} \hspace{0.2in}\mathrm{(quartic).}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5063}%
|
|
$1/100$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4614}%
|
|
\begin{figure}\psfig{file=figs/fig04.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath5039}%
|
|
\begin{displaymath}
|
|
y[n] = f(n/N) .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4622}%
|
|
\begin{figure}\psfig{file=figs/fig04.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4637}%
|
|
\begin{figure}\psfig{file=figs/fig04.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4651}%
|
|
\begin{figure}\psfig{file=figs/fig04.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4657}%
|
|
\begin{figure}\psfig{file=figs/fig04.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4669}%
|
|
\begin{figure}\psfig{file=figs/fig04.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4680}%
|
|
\begin{figure}\psfig{file=figs/fig04.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4686}%
|
|
\begin{figure}\psfig{file=figs/fig04.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5349}%
|
|
\fbox{ $ \mathrm{inlet} $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5351}%
|
|
\fbox{ $ \mathrm{inlet}\sim $}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5359}%
|
|
\fbox{ $\mathrm{outlet}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5361}%
|
|
\fbox{ $\mathrm{outlet}\sim$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4726}%
|
|
\begin{figure}\psfig{file=figs/fig04.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4742}%
|
|
\begin{figure}\psfig{file=figs/fig04.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4751}%
|
|
\begin{figure}\psfig{file=figs/fig04.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4759}%
|
|
\begin{figure}\psfig{file=figs/fig04.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4768}%
|
|
\begin{figure}\psfig{file=figs/fig04.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5433}%
|
|
\fbox{ $\mathrm{unpack}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4783}%
|
|
\begin{figure}\psfig{file=figs/fig04.16.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4788}%
|
|
\begin{figure}\psfig{file=figs/fig04.17.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5463}%
|
|
\fbox{ \texttt{catch\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5465}%
|
|
\fbox{$\mathrm{catch\sim}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5469}%
|
|
\fbox{ \texttt{throw\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5471}%
|
|
\fbox{$\mathrm{throw\sim}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5145}%
|
|
$fp+d$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4819}%
|
|
\begin{figure}\psfig{file=figs/fig04.18.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4824}%
|
|
\begin{figure}\psfig{file=figs/fig04.19.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4837}%
|
|
\begin{figure}\psfig{file=figs/fig04.20.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure4842}%
|
|
\begin{figure}\psfig{file=figs/fig04.21.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5531}%
|
|
\fbox{ $\mathrm{mod}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5535}%
|
|
\fbox{$\mathrm{div}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5539}%
|
|
\fbox{ $\mathrm{poly}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5545}%
|
|
\fbox{ \texttt{makenote}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5547}%
|
|
\fbox{$\mathrm{makenote}$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5167}%
|
|
$f(x) = {x^n}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline5169}%
|
|
$-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5597}%
|
|
\begin{figure}\psfig{file=figs/fig05.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6147}%
|
|
$0:1:2:\cdots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6003}%
|
|
\begin{displaymath}
|
|
{a_0} = {a_0}\cos(0 \cdot \omega n),
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6149}%
|
|
$0:1:2\cdots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6151}%
|
|
$harmonic$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6153}%
|
|
$inharmonic$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6004}%
|
|
\begin{displaymath}
|
|
a \cos (\omega n + \phi)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6155}%
|
|
$a/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6159}%
|
|
$\omega = \phi = 0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6005}%
|
|
\begin{displaymath}
|
|
\cos(a) \cos (b) = {1 \over 2}
|
|
{ \left [
|
|
\parbox[t][0.1in]{0in}{\mbox{}}
|
|
\cos (a+b) + \cos(a-b)
|
|
\right ] }
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6006}%
|
|
\begin{displaymath}
|
|
\cos(a+b) = \cos(a)\cos(b) - \sin(a) \sin(b)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6007}%
|
|
\begin{displaymath}
|
|
{\cos(\alpha n + \phi) \cos (\beta n + \xi)}
|
|
=
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6008}%
|
|
\begin{displaymath}
|
|
= {1 \over 2} { \left [ {
|
|
\parbox[t][0.1in]{0in}{\mbox{}}
|
|
{\cos \left ( (\alpha + \beta) n + (\phi + \xi) \right ) }
|
|
+
|
|
{\cos \left ( (\alpha - \beta) n + (\phi - \xi) \right ) }
|
|
} \right ] }
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6163}%
|
|
$\alpha-\beta$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5647}%
|
|
\begin{figure}\psfig{file=figs/fig05.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6009}%
|
|
\begin{displaymath}
|
|
\left [ 2 a \cos (\alpha n) \right ]
|
|
\cdot
|
|
\left [ \cos (\beta n) \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5653}%
|
|
\begin{figure}\psfig{file=figs/fig05.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6195}%
|
|
$\alpha + \beta$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6199}%
|
|
$\alpha-\beta<0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6010}%
|
|
\begin{displaymath}
|
|
\cos((\alpha - \beta)n) = \cos((\beta - \alpha)n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6201}%
|
|
$\beta-\alpha$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6011}%
|
|
\begin{displaymath}
|
|
{2 a \cos(\alpha n + \phi) \cos (\alpha n + \xi)}
|
|
=
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6012}%
|
|
\begin{displaymath}
|
|
=
|
|
{a \cos \left ( 2 \alpha n + (\phi + \xi) \right ) }
|
|
+
|
|
{a \cos \left ( \phi - \xi \right ) }
|
|
.
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6209}%
|
|
$+a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6211}%
|
|
$-a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6213}%
|
|
$\phi - \xi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6013}%
|
|
\begin{displaymath}
|
|
{a_1} \cos({\alpha _1} n ) + \cdots + {a_k} \cos({\alpha _k} n )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6014}%
|
|
\begin{displaymath}
|
|
\alpha_1 + \beta, \alpha_1 - \beta, \ldots,
|
|
\alpha_k + \beta, \alpha_k - \beta
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6229}%
|
|
$\cdots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5667}%
|
|
\begin{figure}\psfig{file=figs/fig05.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5679}%
|
|
\begin{figure}\psfig{file=figs/fig05.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5691}%
|
|
\begin{figure}\psfig{file=figs/fig05.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6015}%
|
|
\begin{displaymath}
|
|
f(x) = {x^2}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6017}%
|
|
\begin{displaymath}
|
|
f(x[n]) = {{a^2} \over 2} \left ( 1 + \cos(2 \omega n + 2 \phi) \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5699}%
|
|
\begin{figure}\psfig{file=figs/fig05.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6018}%
|
|
\begin{displaymath}
|
|
x[n] = a \cos(\alpha n) + b \cos(\beta n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6019}%
|
|
\begin{displaymath}
|
|
f(x[n]) = {{a^2} \over 2} \left ( 1 + \cos(2 \alpha n) \right ) +
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6020}%
|
|
\begin{displaymath}
|
|
+ {{b^2} \over 2} \left ( 1 + \cos(2 \beta n) \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6021}%
|
|
\begin{displaymath}
|
|
+ a b \left [
|
|
\cos ( (\alpha + \beta) n ) + \cos ( (\alpha - \beta) n )
|
|
\right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6022}%
|
|
\begin{displaymath}
|
|
f(x+y) = {x^2} + 2 x y + {y^2}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6257}%
|
|
$({k^2}-k)/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6024}%
|
|
\begin{displaymath}
|
|
f(x[n+\tau]) = f(x[n])
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6025}%
|
|
\begin{displaymath}
|
|
x[t + \tau/3] = x[t]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6026}%
|
|
\begin{displaymath}
|
|
y[t + \tau/4] = y[t]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6027}%
|
|
\begin{displaymath}
|
|
x[t + \tau] + y[t+\tau] = x[t] + y[t]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6269}%
|
|
$f(x+y)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6028}%
|
|
\begin{displaymath}
|
|
f(x+y)[n + \tau] = f(x+y)[n].
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6029}%
|
|
\begin{displaymath}
|
|
f(x) = {f_0} + {f_1}x + {f_2}{x^2} + {f_3}{x^3} + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6277}%
|
|
$\cos(\omega n)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6030}%
|
|
\begin{displaymath}
|
|
f(a \cdot x[n]) = {f_0} + a {f_1}\cos(\omega n) + {a^2} {f_2} {\cos^2} (\omega n)
|
|
+ {a^3} {f_3} {\cos^3} (\omega n) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6031}%
|
|
\begin{displaymath}
|
|
1 = \cos (0)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6032}%
|
|
\begin{displaymath}
|
|
x[n] = \cos (\omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6033}%
|
|
\begin{displaymath}
|
|
{x^2}[n] = {1 \over 2} + {1 \over 2} \cos (2\omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6034}%
|
|
\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}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6035}%
|
|
\begin{displaymath}
|
|
{x^4}[n] = {1 \over 8} \cos (-2\omega n) + {3 \over 8} \cos (0)
|
|
+ {3 \over 8} \cos (2 \omega n) + {1 \over 8} \cos (4 \omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6036}%
|
|
\begin{displaymath}
|
|
{x^5}[n] = {1 \over 16} \cos (-3\omega n) + {4 \over 16} \cos (-\omega n)
|
|
+ {6 \over 16} \cos (\omega n) + {4 \over 16} \cos (3 \omega n)
|
|
+ {1 \over 16} \cos (5 \omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6287}%
|
|
$f_k$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6037}%
|
|
\begin{displaymath}
|
|
f(x) = {f_0} + {f_2}{x^2} + {f_4}{x^4} + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6295}%
|
|
$f(x)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6038}%
|
|
\begin{displaymath}
|
|
f(-x) = f(x)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6039}%
|
|
\begin{displaymath}
|
|
f(-x) = -f(x)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6303}%
|
|
$\omega_m$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6305}%
|
|
$\omega_c$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6307}%
|
|
$(1-r)\omega_c $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6309}%
|
|
$(1+r) \omega_c$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6313}%
|
|
$r$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6040}%
|
|
\begin{displaymath}
|
|
x[n] = \cos(a \cos(\omega_m n) + \omega_c n )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6327}%
|
|
$a=0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5777}%
|
|
\begin{figure}\psfig{file=figs/fig05.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6041}%
|
|
\begin{displaymath}
|
|
x[n] = \cos(\omega_c n) * \cos(a \cos(\omega_m n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6042}%
|
|
\begin{displaymath}
|
|
- \sin(\omega_c n) * \sin(a \cos(\omega_m n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6339}%
|
|
$f(x) = \cos(x)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6341}%
|
|
$f(x) = \sin(x)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6043}%
|
|
\begin{displaymath}
|
|
\cos(a \cos(\omega_m n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6044}%
|
|
\begin{displaymath}
|
|
\sin(a \cos(\omega_m n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6045}%
|
|
\begin{displaymath}
|
|
0, 2\omega_m, 4\omega_m, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6046}%
|
|
\begin{displaymath}
|
|
\omega_m, 3\omega_m, 5\omega_m, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6047}%
|
|
\begin{displaymath}
|
|
\omega_c + m \omega_m
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6048}%
|
|
\begin{displaymath}
|
|
m = \ldots -2, -1, 0, 1, 2, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6349}%
|
|
$k \tau$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6351}%
|
|
$m \tau$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6357}%
|
|
$km\tau$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6359}%
|
|
$\omega_m=k\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6361}%
|
|
$\omega_c=m\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5790}%
|
|
\begin{figure}\psfig{file=figs/fig05.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5801}%
|
|
\begin{figure}\psfig{file=figs/fig05.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6685}%
|
|
\fbox{ \texttt{fiddle\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6687}%
|
|
\fbox{$\mathrm{fiddle}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5815}%
|
|
\begin{figure}\psfig{file=figs/fig05.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6703}%
|
|
\fbox{ \texttt{clip\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6705}%
|
|
\fbox{$\mathrm{clip}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6379}%
|
|
$300m+225n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5827}%
|
|
\begin{figure}\psfig{file=figs/fig05.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6049}%
|
|
\begin{displaymath}
|
|
\cos(5 \omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6387}%
|
|
$f(x) = x^5$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6051}%
|
|
\begin{displaymath}
|
|
16 {x^5} = \cos (5 \omega n) + 5 \cos(3 \omega n) + 10 \cos(\omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6389}%
|
|
$x^3$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6052}%
|
|
\begin{displaymath}
|
|
16 {x^5} - 20 {x^3} = \cos (5 \omega n) - 5 \cos(\omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6053}%
|
|
\begin{displaymath}
|
|
16 {x^5} - 20 {x^3} + 5 x = \cos (5 \omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6054}%
|
|
\begin{displaymath}
|
|
f(x) = 16 {x^5} - 20 {x^3} + 5 x
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6055}%
|
|
\begin{displaymath}
|
|
x[n] = f( a[n] \cos(\omega n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6395}%
|
|
$a[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6403}%
|
|
$f(x) = x^k$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6056}%
|
|
\begin{displaymath}
|
|
f(x) = {f_0} + {f_1} x + {f_2} {x^2} + \cdots,
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6409}%
|
|
$x^k$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6411}%
|
|
$f_0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6413}%
|
|
$af_1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6415}%
|
|
${a^2}{f_2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6421}%
|
|
$0<a<1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6425}%
|
|
$1<a<2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6429}%
|
|
$2<a<3$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6057}%
|
|
\begin{displaymath}
|
|
{f_1} = {f_0} , 2 {f_2} = {f_1}, 3 {f_3} = {f_2} , \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6435}%
|
|
${f_0}=0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6437}%
|
|
${f_1}=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6439}%
|
|
${f_2}=1/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6441}%
|
|
${f_3}=1/6$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6058}%
|
|
\begin{displaymath}
|
|
{f_k} = {1 \over {1 \cdot 2 \cdot 3 \cdot ... \cdot k}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6059}%
|
|
\begin{displaymath}
|
|
f(x) = {e ^ x}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6443}%
|
|
$e \approx 2.7$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6445}%
|
|
$e^x$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6453}%
|
|
$e^a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6060}%
|
|
\begin{displaymath}
|
|
f(a \cos(\omega n)) =
|
|
{{{e^{a \cos(\omega n)}}} \over {e^a}} = {e^{a (\cos(\omega n) - 1)}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6457}%
|
|
$a=$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5874}%
|
|
\begin{figure}\psfig{file=figs/fig05.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6061}%
|
|
\begin{displaymath}
|
|
f(x) = \cos(x + \phi)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6461}%
|
|
$\phi=-\pi/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6062}%
|
|
\begin{displaymath}
|
|
\cos(a \cos(\omega n)) = {J_0}(a)
|
|
- 2 {J_2}(a) \cos(2 \omega n)
|
|
+ 2 {J_4}(a) \cos(4 \omega n)
|
|
- 2 {J_6}(a) \cos(6 \omega n) \pm \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6063}%
|
|
\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}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6463}%
|
|
${J_k}(a)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6064}%
|
|
\begin{displaymath}
|
|
f(x) = \cos(x) \cos(\phi) - \sin(x) \sin(\phi)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5892}%
|
|
\begin{figure}\psfig{file=figs/fig05.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6065}%
|
|
\begin{displaymath}
|
|
x[t] = \cos( \omega_c n + a \cos(\omega_m n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5901}%
|
|
\begin{figure}\psfig{file=figs/fig05.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6066}%
|
|
\begin{displaymath}
|
|
x[t] = \cos( \omega_c n ) \cos (a \cos(\omega_m n))
|
|
- \sin( \omega_c n ) \sin (a \cos(\omega_m n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6067}%
|
|
\begin{displaymath}
|
|
x[t] = {J_0}(a) \cos( \omega_c n )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6068}%
|
|
\begin{displaymath}
|
|
+ {J_1}(a) \cos( (\omega_c+\omega_m) n + {\pi\over2})
|
|
+ {J_1}(a) \cos( (\omega_c-\omega_m) n + {\pi\over2})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6069}%
|
|
\begin{displaymath}
|
|
+ {J_2}(a) \cos( (\omega_c+2\omega_m) n + \pi)
|
|
+ {J_2}(a) \cos( (\omega_c-2\omega_m) n + \pi)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6070}%
|
|
\begin{displaymath}
|
|
+ {J_3}(a) \cos( (\omega_c+3\omega_m) n + {{3\pi}\over2})
|
|
+ {J_3}(a) \cos( (\omega_c-3\omega_m) n + {{3\pi}\over2})
|
|
+ \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure5919}%
|
|
\begin{figure}\psfig{file=figs/fig05.16.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6489}%
|
|
$\omega_p$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6071}%
|
|
\begin{displaymath}
|
|
x[n] = \cos(\omega_c n + a \cos(\omega_m n) + b \cos(\omega_p n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6491}%
|
|
$\omega_c n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6493}%
|
|
$\omega_c n + b \cos(\omega_p n)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6072}%
|
|
\begin{displaymath}
|
|
{J_3}(a) \cos( (\omega_c+3\omega_m) n + {{3\pi}\over2} + b \cos(\omega_p n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6073}%
|
|
\begin{displaymath}
|
|
\omega_c+3\omega_m + k \omega_p , k = 0, \pm 1, \pm 2, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6495}%
|
|
${J_3}(a) {J_k}(b)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6497}%
|
|
$(3+k)\pi / 2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline6499}%
|
|
$\approx$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath6074}%
|
|
\begin{displaymath}
|
|
\cos( \omega_c n + a \cos( \omega_m n + b \cos( \omega_p n )))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6802}%
|
|
\begin{figure}\psfig{file=figs/fig06.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7115}%
|
|
\begin{displaymath}
|
|
x[n] = \cos(\omega_c n) f (a \cos(\omega_m n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7157}%
|
|
$f (a \cdot \cos(\omega_m n))$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6816}%
|
|
\begin{figure}\psfig{file=figs/fig06.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7116}%
|
|
\begin{displaymath}
|
|
x(\phi) = T (c \phi) * W (a \phi),
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7167}%
|
|
$-\pi \le \phi \le \pi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7169}%
|
|
$T$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6826}%
|
|
\begin{figure}\psfig{file=figs/fig06.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7117}%
|
|
\begin{displaymath}
|
|
x[n] = c(\omega n) {m_a}(\omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7185}%
|
|
${m_a}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7118}%
|
|
\begin{displaymath}
|
|
{m_a}[n] = f (a \cos(\omega n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7195}%
|
|
$f(0)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7203}%
|
|
$f(x) = {e^x}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7119}%
|
|
\begin{displaymath}
|
|
{m_a}[n] = {e^{a \cdot (\cos(\omega n) - 1))}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7120}%
|
|
\begin{displaymath}
|
|
= e ^ {
|
|
{ -\left [
|
|
b \sin {\omega \over 2}
|
|
\right ] }
|
|
^2
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7207}%
|
|
${b^2}=2a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7121}%
|
|
\begin{displaymath}
|
|
{m_a}[n] = g ( b \sin {\omega \over 2} n )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7122}%
|
|
\begin{displaymath}
|
|
g(x) = e ^ {- x ^ 2}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7123}%
|
|
\begin{displaymath}
|
|
h(x) = {1\over{1 + {x^2}}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7124}%
|
|
\begin{displaymath}
|
|
h(b \sin({\omega \over 2} n)) =
|
|
G \cdot \left (
|
|
{1\over 2} + H \cos(\omega n) + {H^2} \cos(2 \omega n)
|
|
+ \cdots
|
|
\right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7211}%
|
|
$G$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7221}%
|
|
$1/(1+b)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7229}%
|
|
${m_a}(\omega n)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7125}%
|
|
\begin{displaymath}
|
|
{M_a}(\phi) = W (a \phi),
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7233}%
|
|
$\omega n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7235}%
|
|
$-\pi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7126}%
|
|
\begin{displaymath}
|
|
W(\phi) = {1\over2} \left ( \cos(\phi) + 1 \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7247}%
|
|
$W(\phi)=(1+\cos(\phi))/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6861}%
|
|
\begin{figure}\psfig{file=figs/fig06.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7255}%
|
|
$1/a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7127}%
|
|
\begin{displaymath}
|
|
\cos(6 \omega n) {M_a}(\omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7261}%
|
|
$M_a$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6872}%
|
|
\begin{figure}\psfig{file=figs/fig06.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6883}%
|
|
\begin{figure}\psfig{file=figs/fig06.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6892}%
|
|
\begin{figure}\psfig{file=figs/fig06.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7267}%
|
|
$\omega_b$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7269}%
|
|
${\omega_c}/\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7271}%
|
|
${\omega_b}/\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7128}%
|
|
\begin{displaymath}
|
|
c(\phi) = c(\omega n) = p \cos( k \omega n) + q \cos( (k+1) \omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7273}%
|
|
$p + q = 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7129}%
|
|
\begin{displaymath}
|
|
(k + q) * {\omega} = {\omega_c}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7281}%
|
|
$q$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7283}%
|
|
$\omega_c/\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7305}%
|
|
$c(\phi)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7315}%
|
|
$c(\phi) = 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7130}%
|
|
\begin{displaymath}
|
|
p \cos ( n {\omega_2} t + r \cos ({\omega_1} t)) +
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7131}%
|
|
\begin{displaymath}
|
|
+ q \cos ( (n+1) {\omega_2} t + r \cos ({\omega_1} t))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7132}%
|
|
\begin{displaymath}
|
|
x[n] = {
|
|
{\underbrace
|
|
{g \left ( a \sin (\omega n/2) \right )}_{\mathrm{modulator}}
|
|
}
|
|
\;
|
|
{\underbrace {\left [
|
|
{p \cos( k \omega n) + q \cos( (k+1) \omega n)}
|
|
\right ] } _\mathrm{carrier}}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6917}%
|
|
\begin{figure}\psfig{file=figs/fig06.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7349}%
|
|
$\sin({\omega \over 2})$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath7133}%
|
|
\begin{displaymath}
|
|
\left | \sin({\omega \over 2}) \right |
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7361}%
|
|
$k+1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7371}%
|
|
$1-q$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6926}%
|
|
\begin{figure}\psfig{file=figs/fig06.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7393}%
|
|
$(k+q)\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7403}%
|
|
$1+b$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6937}%
|
|
\begin{figure}\psfig{file=figs/fig06.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6943}%
|
|
\begin{figure}\psfig{file=figs/fig06.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6948}%
|
|
\begin{figure}\vspace*{-15pt}
|
|
\centerline{\psfig{file=figs/fig06.11.ps,width=3.8in}}
|
|
\vspace*{-13pt}
|
|
|
|
\vspace*{13pt}
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6960}%
|
|
\begin{figure}\psfig{file=figs/fig06.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6965}%
|
|
\begin{figure}\psfig{file=figs/fig06.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7407}%
|
|
$-0.5$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7409}%
|
|
$0.5$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6974}%
|
|
\begin{figure}\psfig{file=figs/fig06.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6984}%
|
|
\begin{figure}\psfig{file=figs/fig06.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure6992}%
|
|
\begin{figure}\psfig{file=figs/fig06.16.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7427}%
|
|
$p
|
|
{c_1} + q {c_2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7431}%
|
|
$c_2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7433}%
|
|
$p=1-q$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7435}%
|
|
${c_1} + q ({c_2} - {c_1})$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7003}%
|
|
\begin{figure}\psfig{file=figs/fig06.17.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7013}%
|
|
\begin{figure}\psfig{file=figs/fig06.18.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline7715}%
|
|
\fbox{ $\mathrm{until}$\ }%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8550}%
|
|
\begin{displaymath}
|
|
Z = a + bi
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8722}%
|
|
$i=\sqrt{-1}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8551}%
|
|
\begin{displaymath}
|
|
a = \mathrm{re}(Z)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8552}%
|
|
\begin{displaymath}
|
|
b = \mathrm{im}(Z)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7770}%
|
|
\begin{figure}\psfig{file=figs/fig07.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8744}%
|
|
$|Z|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8746}%
|
|
$(a,b)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8553}%
|
|
\begin{displaymath}
|
|
|Z| = \sqrt {({a^2} + {b^2})}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8748}%
|
|
$\angle(Z)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8554}%
|
|
\begin{displaymath}
|
|
\angle(Z) = \mathrm{arctan}
|
|
{ \left ( {
|
|
b \over a
|
|
} \right ) }
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8756}%
|
|
$\theta$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8555}%
|
|
\begin{displaymath}
|
|
a = r \cos (\theta)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8556}%
|
|
\begin{displaymath}
|
|
b = r \sin (\theta)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8762}%
|
|
$Z=a+bi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8557}%
|
|
\begin{displaymath}
|
|
Z = r \cdot \left[ \cos(\theta) + i \sin(\theta) \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8776}%
|
|
$Z_1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8778}%
|
|
$Z_2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8558}%
|
|
\begin{displaymath}
|
|
{Z_1} = {r_1} \cdot \left [ \cos({\theta_1}) + i \sin({\theta_1}) \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8559}%
|
|
\begin{displaymath}
|
|
{Z_2} = {r_2} \cdot \left [ \cos({\theta_2}) + i \sin({\theta_2}) \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8560}%
|
|
\begin{displaymath}
|
|
{Z_1}{Z_2} = {r_1}{r_2} \cdot
|
|
{ \left [ {
|
|
\cos({\theta_1}) \cos({\theta_2}) -
|
|
\sin({\theta_1}) \sin({\theta_2})
|
|
} \right . } \, +
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8561}%
|
|
\begin{displaymath}
|
|
{ \left . {
|
|
+ i \left (
|
|
\sin({\theta_1}) \cos({\theta_2}) +
|
|
\cos({\theta_1}) \sin({\theta_2})
|
|
\right )
|
|
} \right ] }
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8780}%
|
|
$\sin({\theta_1}) \sin({\theta_2})$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8782}%
|
|
$i$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8562}%
|
|
\begin{displaymath}
|
|
{Z_1}{Z_2} = {r_1}{r_2}
|
|
\cdot \left[ \cos({\theta_1}+{\theta_2})
|
|
+ i \sin({\theta_1}+{\theta_2}) \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8786}%
|
|
${Z_1}{Z_2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8788}%
|
|
${r_1}{r_2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8790}%
|
|
${\theta_1}+{\theta_2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7827}%
|
|
\begin{figure}\psfig{file=figs/fig07.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8564}%
|
|
\begin{displaymath}
|
|
Z = \cos(\omega) + i \sin(\omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8808}%
|
|
$Z^n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8810}%
|
|
$n\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8565}%
|
|
\begin{displaymath}
|
|
{Z^n} = \cos(n\omega) + i \sin(n \omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8566}%
|
|
\begin{displaymath}
|
|
{1 \over Z} = {Z^{-1}} = cos(\omega) - i \sin(\omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8567}%
|
|
\begin{displaymath}
|
|
\ldots, {Z^0}, {Z^1}, {Z^2}, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8568}%
|
|
\begin{displaymath}
|
|
\ldots, \cos(0), \cos(\omega), \cos(2 \omega), \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8569}%
|
|
\begin{displaymath}
|
|
\ldots, A, AZ, A{Z^2}, \ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8826}%
|
|
$n \omega + \phi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8570}%
|
|
\begin{displaymath}
|
|
{AZ^n} = a \cdot [\cos(n \omega + \phi) + i \sin(n \omega + \phi)]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8571}%
|
|
\begin{displaymath}
|
|
\mathrm{re}(A{Z^n}) = a \cdot \cos(n \omega + \phi)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8838}%
|
|
$A, AZ, A{Z^2}, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8840}%
|
|
$1, Z, {Z^2}, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8572}%
|
|
\begin{displaymath}
|
|
X[n] = A {Z^n} , \ Y[n] = B {Z^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8573}%
|
|
\begin{displaymath}
|
|
X[n] + Y[n] = (A+B) {Z^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8848}%
|
|
$|A+B|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8850}%
|
|
$\angle(A+B)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8852}%
|
|
$X[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8854}%
|
|
$X$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8574}%
|
|
\begin{displaymath}
|
|
Y[n] = X[n-d]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8860}%
|
|
$Y$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8878}%
|
|
${X_1}+{X_2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8575}%
|
|
\begin{displaymath}
|
|
X[n] = A {Z^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8576}%
|
|
\begin{displaymath}
|
|
Y[n] = X[n-d] = A {Z^{(n-d)}} = {Z^{-d}} A {Z^n} = {Z^{-d}} X[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8884}%
|
|
${Z^{-d}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8888}%
|
|
$- d \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8890}%
|
|
$\omega = \angle(Z)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7865}%
|
|
\begin{figure}\psfig{file=figs/fig07.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8900}%
|
|
$d/R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7880}%
|
|
\begin{figure}\psfig{file=figs/fig07.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8910}%
|
|
$x[0]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8912}%
|
|
$x[1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8577}%
|
|
\begin{displaymath}
|
|
X[n] = {Z^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8578}%
|
|
\begin{displaymath}
|
|
H {Z^N}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8579}%
|
|
\begin{displaymath}
|
|
{Z^n} + {Z^{-d}} {Z^n} = (1 + {Z^{-d}}) {Z^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8580}%
|
|
\begin{displaymath}
|
|
H = 1 + {Z^{-d}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7896}%
|
|
\begin{figure}\psfig{file=figs/fig07.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8944}%
|
|
$\cos(-d \omega)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8946}%
|
|
$\sin(-d \omega)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8954}%
|
|
${Z^{d/2}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8956}%
|
|
${Z^{-d/2}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8962}%
|
|
$Z^d$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8964}%
|
|
$Z^{-d}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8966}%
|
|
${Z^{d}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8581}%
|
|
\begin{displaymath}
|
|
H = {Z^{-d/2}} ({Z^{d/2}} + {Z^{-d/2}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8970}%
|
|
$-d \omega / 2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8582}%
|
|
\begin{displaymath}
|
|
{Z^{d/2}} + {Z^{-d/2}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8583}%
|
|
\begin{displaymath}
|
|
= (\cos(\omega d / 2) + i \sin(\omega d / 2)) +
|
|
(\cos(\omega d / 2) - i \sin(\omega d / 2))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8584}%
|
|
\begin{displaymath}
|
|
= 2 \cos(\omega d / 2)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8585}%
|
|
\begin{displaymath}
|
|
|H| = 2 |\cos(\omega d / 2) |
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7926}%
|
|
\begin{figure}\psfig{file=figs/fig07.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8980}%
|
|
$\omega d $%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8988}%
|
|
$2\pi/d$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8990}%
|
|
$\omega = \pi/d$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8994}%
|
|
$d=\pi/\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline8996}%
|
|
$2\omega, 4\omega, 6\omega, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7938}%
|
|
\begin{figure}\psfig{file=figs/fig07.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7946}%
|
|
\begin{figure}\psfig{file=figs/fig07.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8586}%
|
|
\begin{displaymath}
|
|
X[n] = Z^n
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8587}%
|
|
\begin{displaymath}
|
|
Y[n] = (1 + g{Z^{-d}} + {g^2}{Z^{-2d}} + \cdots) X[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8588}%
|
|
\begin{displaymath}
|
|
H = 1 + g{Z^{-d}} + {(g{Z^{-d}})} ^ 2 + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9014}%
|
|
$g{Z^{-d}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8589}%
|
|
\begin{displaymath}
|
|
g{Z^{-d}} H = g{Z^{-d}} + {(g{Z^{-d}})} ^ 2 + {(g{Z^{-d}})} ^ 3 + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8590}%
|
|
\begin{displaymath}
|
|
H - g{Z^{-d}} H = 1
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8591}%
|
|
\begin{displaymath}
|
|
H = {1 \over {1 - g{Z^{-d}}}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9022}%
|
|
$Y[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8592}%
|
|
\begin{displaymath}
|
|
Y[n] \cdot g{Z^{-d}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8593}%
|
|
\begin{displaymath}
|
|
Y[n] = X[n]+Y[n] \cdot g{Z^{-d}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9028}%
|
|
$H=Y[n]/X[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8594}%
|
|
\begin{displaymath}
|
|
H = 1 + Hg{Z^{-d}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8595}%
|
|
\begin{displaymath}
|
|
|H| = {1 \over {|1 - g{Z^{-d}}|}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7974}%
|
|
\begin{figure}\psfig{file=figs/fig07.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure7979}%
|
|
\begin{figure}\psfig{file=figs/fig07.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9054}%
|
|
$|H(\omega)|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8596}%
|
|
\begin{displaymath}
|
|
{Z^{-d}} = 1
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9062}%
|
|
$\omega = 0, 2\pi/d , 4\pi/d , \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8597}%
|
|
\begin{displaymath}
|
|
|H| = {1 \over {1 - g}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9064}%
|
|
$W^n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9066}%
|
|
$\angle(W)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9072}%
|
|
$gW^{-d}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9074}%
|
|
$\sqrt{2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9082}%
|
|
$1-g$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8598}%
|
|
\begin{displaymath}
|
|
\pm(1-g) \approx \mathrm{im}({gW^{-d}}) \approx \angle({W^{-d}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8599}%
|
|
\begin{displaymath}
|
|
(1-g)/d
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9100}%
|
|
$d=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8001}%
|
|
\begin{figure}\psfig{file=figs/fig07.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8600}%
|
|
\begin{displaymath}
|
|
P(x[n]) = \left [{{|x[0]|}^2} + {{|x[1]|}^2} + \cdots
|
|
+ {{|x[N-1]|}^2} \right ] / N
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8601}%
|
|
\begin{displaymath}
|
|
P({x_1}[n] , \ldots , {x_r}[n]) = P({x_1}[n]) + \cdots + P({x_r}[n])
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9114}%
|
|
${x_1}[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9116}%
|
|
${x_r}[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9124}%
|
|
$(0, \ldots, 0)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8602}%
|
|
\begin{displaymath}
|
|
{|{x_1}|}^2 + \cdots + {|{x_r}|}^2
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9128}%
|
|
$({x_1}, \ldots, {x_r})$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8022}%
|
|
\begin{figure}\psfig{file=figs/fig07.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9132}%
|
|
${x_2}[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8603}%
|
|
\begin{displaymath}
|
|
{y_1}[n] = c {x_1}[n] - s {x_2}[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8604}%
|
|
\begin{displaymath}
|
|
{y_2}[n] = s {x_1}[n] + c {x_2}[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9134}%
|
|
$c, s$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8605}%
|
|
\begin{displaymath}
|
|
c = \cos(\theta)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8606}%
|
|
\begin{displaymath}
|
|
s = \sin(\theta)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9138}%
|
|
$({y_1}, {y_2})$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9140}%
|
|
$({x_1}, {x_2})$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8607}%
|
|
\begin{displaymath}
|
|
{|{y_1}|}^2 + {|{y_2}|}^2 = {|{x_1}|}^2 + {|{x_2}|}^2
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9144}%
|
|
$X={x_1} + {x_2}i$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9146}%
|
|
$Y={y_1} + {y_2}i$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8608}%
|
|
\begin{displaymath}
|
|
Y = XZ
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9154}%
|
|
$|X| = |Y|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8609}%
|
|
\begin{displaymath}
|
|
{y_1}[n] = c {x_1}[n] + s {x_2}[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8610}%
|
|
\begin{displaymath}
|
|
{y_2}[n] = s {x_1}[n] - c {x_2}[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9158}%
|
|
$s = c = \sqrt{1/2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9160}%
|
|
$c=s$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9164}%
|
|
$a = \cos(\theta) = \sin(\theta) = \sqrt{1/2} \approx 0.7071$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8060}%
|
|
\begin{figure}\psfig{file=figs/fig07.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8067}%
|
|
\begin{figure}\psfig{file=figs/fig07.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9172}%
|
|
${x_1}, \ldots {x_k}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9174}%
|
|
${y_1}, \ldots {y_k}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9176}%
|
|
${w_1}, \ldots {w_j}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9178}%
|
|
$j$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9194}%
|
|
$w$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9196}%
|
|
$j=k=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9212}%
|
|
$c = \cos(\theta)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8097}%
|
|
\begin{figure}\psfig{file=figs/fig07.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9214}%
|
|
$g \le 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9226}%
|
|
$t/d$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9228}%
|
|
$20 {\log_{10}} (g)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8611}%
|
|
\begin{displaymath}
|
|
20 {t\over d} {\log_{10}} (g)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8612}%
|
|
\begin{displaymath}
|
|
20 {\mathrm{RT}\over d} {\log_{10}}( g ) = -60
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8613}%
|
|
\begin{displaymath}
|
|
\mathrm{RT} = {{-3d} \over {{\log_{10}}(g) }}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8112}%
|
|
\begin{figure}\psfig{file=figs/fig07.16.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9254}%
|
|
$x[n-d]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9262}%
|
|
$d=1.5$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9266}%
|
|
$x[n-1.5]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9270}%
|
|
$x[n+1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8122}%
|
|
\begin{figure}\psfig{file=figs/fig07.17.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9278}%
|
|
$n - d[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9280}%
|
|
$d[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8614}%
|
|
\begin{displaymath}
|
|
y[n] = n - d[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8616}%
|
|
\begin{displaymath}
|
|
0 < d[n] < D
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8617}%
|
|
\begin{displaymath}
|
|
n > y[n] > n - D.
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8618}%
|
|
\begin{displaymath}
|
|
t[n] = y[n] - y[n-1] = 1 - (d[n] - d[n-1])
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8619}%
|
|
\begin{displaymath}
|
|
x[1.5] = {{-x[0] + 9x[1] + 9 x[2] - x[3]} \over 8}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9312}%
|
|
$1.5$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8620}%
|
|
\begin{displaymath}
|
|
x[n] = \cos(\omega \cdot (n - 1.5))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9314}%
|
|
$x[1.5]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8621}%
|
|
\begin{displaymath}
|
|
x[1.5] = {{9 \cos(\omega/2) - \cos(3 \omega / 2)}\over4}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9316}%
|
|
$\omega = \pi / 2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8141}%
|
|
\begin{figure}\psfig{file=figs/fig07.18.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8149}%
|
|
\begin{figure}\psfig{file=figs/fig07.19.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8622}%
|
|
\begin{displaymath}
|
|
d[n] = {d_0} + a \cos(\omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9318}%
|
|
$d_0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8623}%
|
|
\begin{displaymath}
|
|
t = 1 + a \omega \cos(\omega n - \pi/2)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9324}%
|
|
$1 - a \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9326}%
|
|
$1 + a \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8157}%
|
|
\begin{figure}\psfig{file=figs/fig07.20.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8163}%
|
|
\begin{figure}\psfig{file=figs/fig07.21.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9330}%
|
|
${d_0}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9332}%
|
|
${d_0}+s$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9342}%
|
|
$R/f$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9346}%
|
|
$f/R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8624}%
|
|
\begin{displaymath}
|
|
x[n+1] - x[n] = {f \over R}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8625}%
|
|
\begin{displaymath}
|
|
s \cdot x[n+1] - s \cdot x[n] = {{sf} \over R}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8626}%
|
|
\begin{displaymath}
|
|
t = 1 - {{sf} \over R}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8181}%
|
|
\begin{figure}\psfig{file=figs/fig07.22.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8627}%
|
|
\begin{displaymath}
|
|
f = {{(t - 1) R} \over s}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9372}%
|
|
$R/30$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9374}%
|
|
$R/10$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8192}%
|
|
\begin{figure}\psfig{file=figs/fig07.23.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9840}%
|
|
\fbox{ \texttt{delwrite\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9842}%
|
|
\fbox{$\mathrm{delwrite}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9846}%
|
|
\fbox{ \texttt{delread\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9848}%
|
|
\fbox{$\mathrm{delread}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8206}%
|
|
\begin{figure}\psfig{file=figs/fig07.24.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8213}%
|
|
\begin{figure}\psfig{file=figs/fig07.25.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9876}%
|
|
\fbox{ \texttt{vd\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9878}%
|
|
\fbox{$\mathrm{vd}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8231}%
|
|
\begin{figure}\psfig{file=figs/fig07.26.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8628}%
|
|
\begin{displaymath}
|
|
x[N], \ldots, x[N+B-1] \longrightarrow \fbox{\texttt{delwrite\~}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8629}%
|
|
\begin{displaymath}
|
|
\fbox{\texttt{delread\~}} \longrightarrow x[N], \ldots, x[N+B-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9392}%
|
|
$x[N], \ldots, x[N+B-1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8630}%
|
|
\begin{displaymath}
|
|
\fbox{\texttt{delread\~}} \longrightarrow x[N-B], \ldots, x[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8247}%
|
|
\begin{figure}\psfig{file=figs/fig07.27.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9924}%
|
|
\fbox{ \texttt{block\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9926}%
|
|
\fbox{ \texttt{switch\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9928}%
|
|
\fbox{$\mathrm{block}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9930}%
|
|
\fbox{$\mathrm{switch}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8267}%
|
|
\begin{figure}\psfig{file=figs/fig07.28.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8276}%
|
|
\begin{figure}\psfig{file=figs/fig07.29.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9408}%
|
|
$1000\cdot2048/R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9412}%
|
|
$1000/(2f)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9416}%
|
|
$1/(2f)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9418}%
|
|
$2f, 4f, 6f\cdots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9420}%
|
|
$f, 3f, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9422}%
|
|
$2f$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8285}%
|
|
\begin{figure}\psfig{file=figs/fig07.30.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8299}%
|
|
\begin{figure}\psfig{file=figs/fig07.31.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline9428}%
|
|
$\sqrt{1/2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8305}%
|
|
\begin{figure}\psfig{file=figs/fig07.32.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure8315}%
|
|
\begin{figure}\psfig{file=figs/fig07.33.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8632}%
|
|
\begin{displaymath}
|
|
t = {2 ^ {h/12}} = {e ^ {\log(2)/12 \cdot h}} \approx {e ^ {0.05776 h}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath8633}%
|
|
\begin{displaymath}
|
|
{[ {{(1-g \cos (\omega d))}^2} + {{(g \sin (\omega d))}^2} ]}
|
|
^
|
|
{-1/2}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10050}%
|
|
\begin{figure}\psfig{file=figs/fig08.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11087}%
|
|
$H(\omega)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11095}%
|
|
$\angle( H(\omega))$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10068}%
|
|
\begin{figure}\psfig{file=figs/fig08.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10090}%
|
|
\begin{figure}\psfig{file=figs/fig08.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10100}%
|
|
\begin{figure}\psfig{file=figs/fig08.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10113}%
|
|
\begin{figure}\psfig{file=figs/fig08.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10122}%
|
|
\begin{figure}\psfig{file=figs/fig08.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10136}%
|
|
\begin{figure}\psfig{file=figs/fig08.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11117}%
|
|
$\omega=\arg(Z)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10951}%
|
|
\begin{displaymath}
|
|
(1 - Q{Z^{-1}}){Z^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10952}%
|
|
\begin{displaymath}
|
|
H(Z) = 1 - Q{Z^{-1}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10953}%
|
|
\begin{displaymath}
|
|
Q = r \cdot (\cos(\alpha) + i \sin(\alpha))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10954}%
|
|
\begin{displaymath}
|
|
|1 - Q{Z^{-1}}| = |Z||1 - Q{Z^{-1}}| = |Q - Z|
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11133}%
|
|
$Q{Z^{-1}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11139}%
|
|
$|1 - Q{Z^{-1}}|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10151}%
|
|
\begin{figure}\psfig{file=figs/fig08.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11157}%
|
|
$\omega = \alpha$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11159}%
|
|
$1-r$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10157}%
|
|
\begin{figure}\psfig{file=figs/fig08.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11171}%
|
|
$\overline{Q}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10955}%
|
|
\begin{displaymath}
|
|
A = a+bi = r \cdot (\cos(\alpha) + i \sin(\alpha))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10956}%
|
|
\begin{displaymath}
|
|
\overline{A} = a-bi = r \cdot (\cos(\alpha) - i \sin(\alpha))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10957}%
|
|
\begin{displaymath}
|
|
H(Z) = \overline{Q} - {Z^{-1}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10958}%
|
|
\begin{displaymath}
|
|
|\overline{Q} - {Z^{-1}}| = |Q - \overline{Z^{-1}}| = |Q- Z|
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11173}%
|
|
$\overline{Z} = {Z^{-1}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11177}%
|
|
$Z\overline{Z}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10178}%
|
|
\begin{figure}\psfig{file=figs/fig08.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11179}%
|
|
$P$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10959}%
|
|
\begin{displaymath}
|
|
{{1} \over {1 - P {Z^{-1}}}} {Z^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10960}%
|
|
\begin{displaymath}
|
|
H(Z) = {{1} \over {1 - P {Z^{-1}}}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11185}%
|
|
$|P| < 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11187}%
|
|
$|P|> 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10195}%
|
|
\begin{figure}\psfig{file=figs/fig08.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11189}%
|
|
$P=Q$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11191}%
|
|
${Q_1}, \ldots, {Q_j}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11193}%
|
|
${P_1}, \ldots, {P_k}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10961}%
|
|
\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}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11199}%
|
|
$\overline{P}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10962}%
|
|
\begin{displaymath}
|
|
H(Z) = (1 - {Q}{Z^{-1}}) \cdot (1 - \overline{Q}{Z^{-1}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10963}%
|
|
\begin{displaymath}
|
|
H(\overline{Z}) = \overline{H(Z)}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10964}%
|
|
\begin{displaymath}
|
|
{X_n} = 2 \, \mathrm{re}(A{Z^n}) = A{Z^n} + \overline{A}
|
|
{{\overline{Z}}^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10965}%
|
|
\begin{displaymath}
|
|
A \cdot H(Z) \cdot {Z^n} +
|
|
\overline{A} \cdot \overline{H(Z)} \cdot {{\overline{Z}}^n}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10966}%
|
|
\begin{displaymath}
|
|
\overline{A+B} = \overline{A} + \overline{B}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10967}%
|
|
\begin{displaymath}
|
|
\overline{AB} = \overline{A} \cdot \overline{B}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10968}%
|
|
\begin{displaymath}
|
|
A + \overline{A} = 2 \, \mathrm{re} (A)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11207}%
|
|
$Q_i$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11209}%
|
|
$P_i$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10969}%
|
|
\begin{displaymath}
|
|
A{Z^n} + \overline{A}{Z^{-n}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10970}%
|
|
\begin{displaymath}
|
|
a[n] =
|
|
\mathrm{re} \left[ {
|
|
{1 \over {1 - {P}{Z^{-1}}}} {A{Z^n} +
|
|
{1 \over {1 - {P}{Z}}} \overline{A}{Z^{-n}}}
|
|
} \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10971}%
|
|
\begin{displaymath}
|
|
=
|
|
\mathrm{re} \left[ {
|
|
{1 \over {1 - {P}{Z^{-1}}}} {A{Z^n}} +
|
|
{1 \over {1 - \overline{P}{Z^{-1}}}} {A{Z^n}}
|
|
} \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10972}%
|
|
\begin{displaymath}
|
|
=
|
|
\mathrm{re} \left[ {
|
|
{{
|
|
2 - 2 \, \mathrm{re} (P) {Z^{-1}}
|
|
} \over {
|
|
(1 - {P}{Z^{-1}}) (1 - {\overline{P}}{Z^{-1}})
|
|
}}
|
|
{A{Z^n}}
|
|
} \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10973}%
|
|
\begin{displaymath}
|
|
=
|
|
\mathrm{re} \left[ {
|
|
{{
|
|
1 - \mathrm{re} (P) {Z^{-1}}
|
|
} \over {
|
|
(1 - {P}{Z^{-1}}) (1 - {\overline{P}}{Z^{-1}})
|
|
}}
|
|
{A{Z^n}}
|
|
+
|
|
{{
|
|
1 - \mathrm{re} (P) {{\overline{Z}}^{-1}}
|
|
} \over {
|
|
(1 - {\overline{P}}{{\overline{Z}}^{-1}}) (1 - {P}{{\overline{Z}}^{-1}})
|
|
}}
|
|
{\overline{A}{{\overline{Z}}^{-n}}}
|
|
} \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10974}%
|
|
\begin{displaymath}
|
|
{H_{\mathrm{re}}}(Z) = {{
|
|
1 - \mathrm{re} (P) {Z^{-1}}
|
|
} \over {
|
|
(1 - {P}{Z^{-1}}) (1 - {\overline{P}}{Z^{-1}})
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10975}%
|
|
\begin{displaymath}
|
|
{H_{\mathrm{im}}}(Z) = {{
|
|
\mathrm{im} (P) {Z^{-1}}
|
|
} \over {
|
|
(1 - {P}{Z^{-1}}) (1 - {\overline{P}}{Z^{-1}})
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11235}%
|
|
$1/\overline{Q}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10318}%
|
|
\begin{figure}\psfig{file=figs/fig08.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11243}%
|
|
$1/(1-p)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11247}%
|
|
$1-p$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11255}%
|
|
$p = 1-\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10976}%
|
|
\begin{displaymath}
|
|
H(Z) = 1 - {{{1-p} \over {1 - p{Z^{-1}}}}}
|
|
= p{{{1-{Z^{-1}}} \over {1 - p{Z^{-1}}}}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10336}%
|
|
\begin{figure}\psfig{file=figs/fig08.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10344}%
|
|
\begin{figure}\psfig{file=figs/fig08.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11311}%
|
|
$d = \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11313}%
|
|
$p = 1 - d / \sqrt{g}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11315}%
|
|
$q = 1 - d \sqrt{g}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10977}%
|
|
\begin{displaymath}
|
|
{{1-q} \over {1-p}} = g
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11329}%
|
|
$p = 1 - \beta$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11333}%
|
|
$\cos \omega + i \sin \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10978}%
|
|
\begin{displaymath}
|
|
{P_1} = (1 - \beta) (\cos \omega + i \sin \omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10979}%
|
|
\begin{displaymath}
|
|
{P_2} = \overline{P_1} = (1 - \beta) (\cos \omega - i \sin \omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10359}%
|
|
\begin{figure}\psfig{file=figs/fig08.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10980}%
|
|
\begin{displaymath}
|
|
\beta * (\beta + 2 \omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10981}%
|
|
\begin{displaymath}
|
|
{P_1} = p \cdot (\cos \omega + i \sin \omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10982}%
|
|
\begin{displaymath}
|
|
{Q_1} = q \cdot (\cos \omega + i \sin \omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10369}%
|
|
\begin{figure}\psfig{file=figs/fig08.16.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10983}%
|
|
\begin{displaymath}
|
|
{{1 - {r^2}} \over {{(1 + r)}^2}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11361}%
|
|
$r=0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11365}%
|
|
$r=\infty$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10984}%
|
|
\begin{displaymath}
|
|
{ (1 - {r^2}) - (2 r \sin(\alpha)) i }
|
|
\over
|
|
{ 1 + {r^2} + 2 r \cos(\alpha))}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10985}%
|
|
\begin{displaymath}
|
|
{\pi \over 2} ({1 \over n} - 1) , \;
|
|
{\pi \over 2} ({3 \over n} - 1) , \; \ldots , \;
|
|
{\pi \over 2} ({{2n-1} \over n} - 1)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11381}%
|
|
$\alpha = \pi/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10986}%
|
|
\begin{displaymath}
|
|
{ (1 - {r^2}) - 2 r i }
|
|
\over
|
|
{ 1 + {r^2} }
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10987}%
|
|
\begin{displaymath}
|
|
\beta = 2 \arctan (r)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10391}%
|
|
\begin{figure}\psfig{file=figs/fig08.17.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10397}%
|
|
\begin{figure}\psfig{file=figs/fig08.18.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10989}%
|
|
\begin{displaymath}
|
|
| H(\cos(\omega) + i \sin(\omega)) |
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11405}%
|
|
$R(Z)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11413}%
|
|
$|R(Z)| = 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11415}%
|
|
$Z=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10990}%
|
|
\begin{displaymath}
|
|
R(Z) = U \cdot
|
|
{{
|
|
{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}
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11417}%
|
|
$|U|=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10991}%
|
|
\begin{displaymath}
|
|
J(Z) = H(R(Z))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11427}%
|
|
$J$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10992}%
|
|
\begin{displaymath}
|
|
\cos(\phi) + i \sin(\phi) = R(\cos(\omega) + i \sin(\omega))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10993}%
|
|
\begin{displaymath}
|
|
H(Z) =
|
|
{{
|
|
1 + {Z^{-1}}
|
|
} \over {
|
|
1 - g{Z^{-1}}
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10994}%
|
|
\begin{displaymath}
|
|
R(Z) = -{Z^2} = -
|
|
{{
|
|
1 \cdot {Z^2} + 0 \cdot Z + 0
|
|
} \over {
|
|
0 \cdot {Z^2} + 0 \cdot Z + 1
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11453}%
|
|
$-i$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10995}%
|
|
\begin{displaymath}
|
|
J(Z) =
|
|
{{
|
|
1 - {Z^{-2}}
|
|
} \over {
|
|
1 + g{Z^{-2}}
|
|
}}
|
|
=
|
|
{{
|
|
(1 - {Z^{-1}})(1 + {Z^{-1}})
|
|
} \over {
|
|
(1 - i\sqrt{g} {Z^{-1}})(1 + i\sqrt{g} {Z^{-1}})
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10438}%
|
|
\begin{figure}\psfig{file=figs/fig08.19.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11473}%
|
|
$R(Z) = -Z^2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10996}%
|
|
\begin{displaymath}
|
|
S(Z) =
|
|
{{
|
|
aZ + b
|
|
} \over {
|
|
bZ + a
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11485}%
|
|
$S(1) = 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11487}%
|
|
$S(-1) = -1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11493}%
|
|
$\overline{Z}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11495}%
|
|
$\overline{W}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11497}%
|
|
$S$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10997}%
|
|
\begin{displaymath}
|
|
S(\cos(\omega) + i \sin(\omega)) = i
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11507}%
|
|
$R = - {Z^2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11511}%
|
|
$H(R(S(Z)))$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10998}%
|
|
\begin{displaymath}
|
|
a = \cos({{\pi}\over 4} - {{\omega} \over 2}) , \;
|
|
b = \sin({{\pi}\over 4} - {{\omega} \over 2})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11521}%
|
|
$2n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11531}%
|
|
$J(Z) = H(R(S(Z)))$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11533}%
|
|
$J(Z)=\infty$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11535}%
|
|
$R(S(Z))$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11541}%
|
|
$R(S(Z)) = W$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath10999}%
|
|
\begin{displaymath}
|
|
- {
|
|
{ \left [ {
|
|
{
|
|
aZ + b
|
|
} \over {
|
|
bZ + a
|
|
}
|
|
} \right ] }
|
|
^ 2
|
|
} = W
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11000}%
|
|
\begin{displaymath}
|
|
{
|
|
{
|
|
aZ + b
|
|
} \over {
|
|
bZ + a
|
|
}
|
|
} = {
|
|
\pm \sqrt {
|
|
- W
|
|
}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11001}%
|
|
\begin{displaymath}
|
|
Z = { {
|
|
\pm a \sqrt { - W }
|
|
- b
|
|
} \over {
|
|
\mp b \sqrt { - W }
|
|
+ a
|
|
}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11553}%
|
|
${a^2}+{b^2}=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10463}%
|
|
\begin{figure}\psfig{file=figs/fig08.20.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10470}%
|
|
\begin{figure}\psfig{file=figs/fig08.21.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11561}%
|
|
$1-|P|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11563}%
|
|
$1-1/n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11002}%
|
|
\begin{displaymath}
|
|
{ {\left ( 1-{1\over n} \right ) } ^ n } \approx {1\over e}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11571}%
|
|
$e$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11575}%
|
|
$n=5$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10485}%
|
|
\begin{figure}\psfig{file=figs/fig08.22.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11591}%
|
|
$1/e$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11003}%
|
|
\begin{displaymath}
|
|
{{n} \over {2\pi/\omega}} = {{1} \over {2\pi}} {{\omega} \over {b}}
|
|
= {{q} \over {2\pi}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11615}%
|
|
$P<1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11004}%
|
|
\begin{displaymath}
|
|
H(Z) = {{
|
|
{\overline{P} - {Z^{-1}}}
|
|
} \over {
|
|
{1 - P{Z^{-1}}}
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11621}%
|
|
$1/\overline{P}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10509}%
|
|
\begin{figure}\psfig{file=figs/fig08.23.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10520}%
|
|
\begin{figure}\psfig{file=figs/fig08.24.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10526}%
|
|
\begin{figure}\psfig{file=figs/fig08.25.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11005}%
|
|
\begin{displaymath}
|
|
y[n] = p \cdot y[n-1] + (1-p) \cdot x[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11645}%
|
|
$x[n]^2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10537}%
|
|
\begin{figure}\psfig{file=figs/fig08.26.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11006}%
|
|
\begin{displaymath}
|
|
x[n] = a \cdot \cos(\alpha n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11007}%
|
|
\begin{displaymath}
|
|
{{x[n]}^2} = {{a^2}\over 2} \left ( \cos(2 \alpha n) + 1 \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11647}%
|
|
$2 \alpha$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11649}%
|
|
${{a^2} / 2}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11008}%
|
|
\begin{displaymath}
|
|
x[n] = a \cdot \cos(\alpha n) + b \cdot \cos(\beta n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11651}%
|
|
$({a^2} +
|
|
{b^2})/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10549}%
|
|
\begin{figure}\psfig{file=figs/fig08.27.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11655}%
|
|
$1, W, {W^2}, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11657}%
|
|
$1, WZ, {{(WZ)}^2}, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11659}%
|
|
$\angle(ZW)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11009}%
|
|
\begin{displaymath}
|
|
x[n] = a \cdot \cos (\omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11010}%
|
|
\begin{displaymath}
|
|
X[n] = a \left ( \cos (\omega n) + i \sin (\omega n) \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11011}%
|
|
\begin{displaymath}
|
|
x[n] = \mathrm{re} (X[n])
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11665}%
|
|
$-\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11012}%
|
|
\begin{displaymath}
|
|
X'[n] = a \left ( \cos (\omega n) - i \sin (\omega n) \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11683}%
|
|
$H_1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11685}%
|
|
$H_2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11013}%
|
|
\begin{displaymath}
|
|
\angle({H_1}(Z)) - \angle({H_2}(Z)) \approx
|
|
\left \{
|
|
\begin{array}{ll}
|
|
\pi/2 & {0 < \angle(Z) < \pi} \\
|
|
-\pi/2 & {-\pi < \angle(Z) < 0}
|
|
\end{array}
|
|
\right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11014}%
|
|
\begin{displaymath}
|
|
{H_1}(Z) \approx i {H_2}(Z) , \; 0 < \angle(Z) < \pi
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11015}%
|
|
\begin{displaymath}
|
|
{H_1}(Z) \approx -i {H_2}(Z) , \; -\pi < \angle(Z) < 0
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11689}%
|
|
$a[n] + i b[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11693}%
|
|
$b[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath11016}%
|
|
\begin{displaymath}
|
|
{H_1}(Z) + i {H_2}(Z) \approx
|
|
\left \{
|
|
\begin{array}{ll}
|
|
2 {H_1}(Z) & {0 < \angle(Z) < \pi} \\
|
|
0 & \mbox{otherwise}
|
|
\end{array}
|
|
\right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12147}%
|
|
\fbox{\texttt{lop\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12149}%
|
|
\fbox{$\mathrm{lop}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12153}%
|
|
\fbox{ \texttt{hip\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12159}%
|
|
\fbox{ \texttt{bp\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12161}%
|
|
\fbox{$\mathrm{bp}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12165}%
|
|
\fbox{ \texttt{noise\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12167}%
|
|
\fbox{$\mathrm{noise}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10598}%
|
|
\begin{figure}\psfig{file=figs/fig08.28.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12183}%
|
|
\fbox{ \texttt{vcf\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12185}%
|
|
\fbox{$\mathrm{vcf}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10610}%
|
|
\begin{figure}\psfig{file=figs/fig08.29.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10620}%
|
|
\begin{figure}\psfig{file=figs/fig08.30.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10626}%
|
|
\begin{figure}\psfig{file=figs/fig08.31.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10639}%
|
|
\begin{figure}\psfig{file=figs/fig08.32.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12231}%
|
|
\fbox{ \texttt{rzero\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12233}%
|
|
\fbox{ \texttt{rzero\_rev\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12235}%
|
|
\fbox{ \texttt{rpole\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12237}%
|
|
\fbox{$\mathrm{rzero}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12239}%
|
|
\fbox{$\mathrm{rzero\_rev}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12241}%
|
|
\fbox{$\mathrm{rpole}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12245}%
|
|
\fbox{ \texttt{czero\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12247}%
|
|
\fbox{ \texttt{czero\_rev\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12249}%
|
|
\fbox{ \texttt{cpole\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12251}%
|
|
\fbox{$\mathrm{czero}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12253}%
|
|
\fbox{$\mathrm{czero\_rev}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline12255}%
|
|
\fbox{$\mathrm{cpole}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure10670}%
|
|
\begin{figure}\psfig{file=figs/fig08.33.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline11727}%
|
|
$i/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13143}%
|
|
$n=0,\ldots,N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13155}%
|
|
$4\pi/N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13159}%
|
|
$2(N-1)\pi/N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13173}%
|
|
$0 \leq k < N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13175}%
|
|
$2\pi k / N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13187}%
|
|
$\omega=2\pi/N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13191}%
|
|
$U$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12979}%
|
|
\begin{displaymath}
|
|
U = \cos(\omega) + i \sin(\omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12980}%
|
|
\begin{displaymath}
|
|
{P_k}[n] = {A_k}{{\left [ {U^k} \right ]} ^ {n}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13199}%
|
|
${A_k}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12981}%
|
|
\begin{displaymath}
|
|
\angle({U^k}) = k \angle(U) = k\omega
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12982}%
|
|
\begin{displaymath}
|
|
X[n] =
|
|
{A_0}{{\left [ {U^0} \right ]} ^ {n}}
|
|
+ {A_1}{{\left [ {U^1} \right ]} ^ {n}}
|
|
+ \cdots
|
|
+ {A_{N-1}}{{\left [ {U^{N-1}} \right ]} ^ {n}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13205}%
|
|
$A_k$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13207}%
|
|
$-k\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12983}%
|
|
\begin{displaymath}
|
|
{A_k} = {1\over N} \left (
|
|
{{\left [ {U^{-k}} \right ]} ^ {0}} X[0] +
|
|
{{\left [ {U^{-k}} \right ]} ^ {1}} X[1] +
|
|
\cdots +
|
|
{{\left [ {U^{-k}} \right ]} ^ {N-1}} X[N-1]
|
|
\right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12984}%
|
|
\begin{displaymath}
|
|
{\cal FT}\left \{ X[n] \right \} (k) =
|
|
{V ^ {0}} X[0] +
|
|
{V ^ {1}} X[1] +
|
|
\cdots +
|
|
{V ^ {N-1}} X[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13213}%
|
|
$V = {U^{-k}}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13225}%
|
|
$V$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12985}%
|
|
\begin{displaymath}
|
|
V = \cos(-k\omega) + i\sin(-k\omega)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12986}%
|
|
\begin{displaymath}
|
|
{\cal FT}\left \{ X[n] \right \} (k+N) =
|
|
{\cal FT}\left \{ X[n] \right \} (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13251}%
|
|
$Y[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13255}%
|
|
$k = 0, ..., N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12988}%
|
|
\begin{displaymath}
|
|
Y[k] = {\cal FT}\left \{ X[n] \right \} (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12989}%
|
|
\begin{displaymath}
|
|
= {{\left [ {U^{-k}} \right ]} ^ {0}} X[0] +
|
|
{{\left [ {U^{-k}} \right ]} ^ {1}} X[1] +
|
|
\cdots +
|
|
{{\left [ {U^{-k}} \right ]} ^ {N-1}} X[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12990}%
|
|
\begin{displaymath}
|
|
= {{\left [ {U^{0}} \right ]} ^ {k}} X[0] +
|
|
{{\left [ {U^{-1}} \right ]} ^ {k}} X[1] +
|
|
\cdots +
|
|
{{\left [ {U^{-(N-1)}} \right ]} ^ {k}} X[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13259}%
|
|
$X[m]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13261}%
|
|
$-m\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13263}%
|
|
$m = 0, \ldots, N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13269}%
|
|
$X[-m]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12991}%
|
|
\begin{displaymath}
|
|
{1 \over N} {\cal FT} \left \{ Y[k] \right \} (m) = X[-m]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13279}%
|
|
$Y[k]/N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13281}%
|
|
$n = -m$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12992}%
|
|
\begin{displaymath}
|
|
X[n] = {1 \over N} {\cal FT} \left \{ Y[k] \right \} (-n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12993}%
|
|
\begin{displaymath}
|
|
= {{\left [ {U^{0}} \right ]} ^ {n}} Y[0] +
|
|
{{\left [ {U^{1}} \right ]} ^ {n}} Y[1] +
|
|
\cdots +
|
|
{{\left [ {U^{N-1}} \right ]} ^ {n}} Y[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13289}%
|
|
$k=0,
|
|
\ldots, N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13291}%
|
|
$X[n]=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13295}%
|
|
$N>1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12994}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ X[n] \right \} (k) =
|
|
\left \{
|
|
\begin{array}{ll}
|
|
N & {k=0} \\
|
|
0 & {k=1, \ldots, N-1}
|
|
\end{array}
|
|
\right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13303}%
|
|
$V \not= 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12996}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ X[n] \right \} (k) =
|
|
{{
|
|
{V^N} - 1
|
|
} \over {
|
|
V - 1
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12997}%
|
|
\begin{displaymath}
|
|
\xi = \cos(\pi k / N) - i \sin(\pi k / N)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13305}%
|
|
${\xi^2} = V$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13307}%
|
|
$\xi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12998}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ X[n] \right \} (k) =
|
|
{\xi^{N-1}}
|
|
{{
|
|
{\xi^N} - {\xi^{-N}}
|
|
} \over {
|
|
\xi - {\xi^{-1}}
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath12999}%
|
|
\begin{displaymath}
|
|
{\xi^N} - {\xi^{-N}} =
|
|
\left (\cos(\pi k) - i \sin(\pi k) \right ) -
|
|
\left (\cos(\pi k) + i \sin(\pi k) \right )
|
|
= - 2 i \sin(\pi k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13000}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ X[n] \right \} (k) =
|
|
\left ( {
|
|
\parbox[t][0.1in]{0in}{\mbox{}}
|
|
\cos(\pi k (N-1)/N) - i \sin(\pi k (N-1)/N)
|
|
} \right )
|
|
{{
|
|
\sin(\pi k)
|
|
} \over {
|
|
\sin(\pi k / N)
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13309}%
|
|
$V=1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13001}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ X[n] \right \} (k) =
|
|
\left ( {
|
|
\parbox[t][0.1in]{0in}{\mbox{}}
|
|
\cos(\pi k (N-1)/N) - i \sin(\pi k (N-1)/N)
|
|
} \right )
|
|
{D_N}(k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13311}%
|
|
${D_N}(k)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13002}%
|
|
\begin{displaymath}
|
|
{D_N}(k) =
|
|
\left \{
|
|
\begin{array}{ll}
|
|
N & {k= 0} \\
|
|
{{
|
|
\sin(\pi k)
|
|
} \over {
|
|
\sin(\pi k / N)
|
|
}}
|
|
& {k\not=0,\; -N < k < N}
|
|
\end{array}
|
|
\right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13317}%
|
|
$k=0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13319}%
|
|
$k=100$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13003}%
|
|
\begin{displaymath}
|
|
\cos(\pi k (N-1)/N) - i \sin(\pi k (N-1)/N)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13321}%
|
|
${\cal FT} \left \{ X[n] \right \} (k)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13335}%
|
|
$k>1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13337}%
|
|
$k < -1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13341}%
|
|
$k=-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12411}%
|
|
\begin{figure}\psfig{file=figs/fig09.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12416}%
|
|
\begin{figure}\psfig{file=figs/fig09.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13005}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ Y[n] \right \} (k) =
|
|
{V ^ {0}} Y[0] +
|
|
{V ^ {1}} Y[1] +
|
|
\cdots +
|
|
{V ^ {N-1}} Y[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13006}%
|
|
\begin{displaymath}
|
|
=
|
|
{V ^ {0}} X[-d] +
|
|
{V ^ {1}} X[-d+1] +
|
|
\cdots +
|
|
{V ^ {N-1}} X[-d+N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13007}%
|
|
\begin{displaymath}
|
|
=
|
|
{V ^ {d}} X[0] +
|
|
{V ^ {d+1}} X[1] +
|
|
\cdots +
|
|
{V ^ {d+N-1}} X[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13008}%
|
|
\begin{displaymath}
|
|
= {V^d} \left (
|
|
{V ^ {0}} X[0] +
|
|
{V ^ {1}} X[1] +
|
|
\cdots +
|
|
{V ^ {N-1}} X[N-1]
|
|
\right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13009}%
|
|
\begin{displaymath}
|
|
= {V^d} {\cal FT} \left \{ X[n] \right \} (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13010}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ X[n-d] \right \} (k) =
|
|
\left ( {
|
|
\parbox[t][0.1in]{0in}{\mbox{}}
|
|
\cos(-dk\omega) + i\sin(-dk\omega)
|
|
} \right )
|
|
{\cal FT} \left \{ X[n] \right \} (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13365}%
|
|
$X[n-d]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13369}%
|
|
$-dk\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13011}%
|
|
\begin{displaymath}
|
|
Y[n] = {Z^n} X[n]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13012}%
|
|
\begin{displaymath}
|
|
Z = \cos(\alpha) + i \sin(\alpha)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13014}%
|
|
\begin{displaymath}
|
|
=
|
|
{V ^ {0}} X[0] +
|
|
{V ^ {1}} Z X[1] +
|
|
\cdots +
|
|
{V ^ {N-1}} {Z^{N-1}} X[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13015}%
|
|
\begin{displaymath}
|
|
=
|
|
{{(VZ)} ^ {0}} X[0] +
|
|
{{(VZ)} ^ {1}} X[1] +
|
|
\cdots +
|
|
{{(VZ)} ^ {N-1}} X[N-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13016}%
|
|
\begin{displaymath}
|
|
= {\cal FT} \left \{ X[n] \right \} (k - {{\alpha } \over {\omega}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13017}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ (\cos(\alpha) + i \sin(\alpha)) X[n] \right \} (k) =
|
|
{\cal FT} \left \{ X[n] \right \} (k - {{\alpha N} \over {2 \pi}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13379}%
|
|
${Z^n}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13018}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ {Z^n} \right \} (k) =
|
|
{\cal FT} \left \{ 1 \right \}(k - {{\alpha } \over {\omega}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13019}%
|
|
\begin{displaymath}
|
|
= \left [ \cos(\Phi(k)) + i \sin(\Phi(k))\right ]
|
|
{D_N}(k - {{\alpha } \over {\omega}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13385}%
|
|
${D_N}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13387}%
|
|
$\Phi$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13020}%
|
|
\begin{displaymath}
|
|
\Phi(k) = - \pi \cdot (k - {{\alpha } \over {\omega}}) \cdot (N-1)/N
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12482}%
|
|
\begin{figure}\psfig{file=figs/fig09.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12488}%
|
|
\begin{figure}\psfig{file=figs/fig09.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13427}%
|
|
$w[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13021}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ w[n] X[n] \right \} (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13022}%
|
|
\begin{displaymath}
|
|
w[n] = {1\over 2} - {1\over 2} \cos(2\pi n / N)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13023}%
|
|
\begin{displaymath}
|
|
w[n] = {1\over 2} - {1\over 4} {U^n} - {1\over 4} {U^{-n}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13024}%
|
|
\begin{displaymath}
|
|
{\cal FT} \left \{ w[n] {Z^n} \right \} (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13025}%
|
|
\begin{displaymath}
|
|
= {\cal FT} \left \{ {1\over 2} {Z^n} - {1\over 4} {(UZ)^n}
|
|
- {1\over 4} {({U^{-1}}Z)^n}\right \} (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13026}%
|
|
\begin{displaymath}
|
|
\approx \left [ \cos(\Phi(k)) + i \sin(\Phi(k))\right ]
|
|
M(k - {{\alpha } \over {\omega}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13027}%
|
|
\begin{displaymath}
|
|
\Phi(k) = - \pi \cdot (k - {{\alpha } \over {\omega}})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13028}%
|
|
\begin{displaymath}
|
|
M(k) =
|
|
{\left [ {
|
|
{1\over 2}{D_N}(k)
|
|
+ {1\over 4}{D_N}(k + 1)
|
|
+ {1\over 4}{D_N}(k - 1)
|
|
} \right ] }
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13437}%
|
|
$M(k)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12534}%
|
|
\begin{figure}\psfig{file=figs/fig09.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13447}%
|
|
${D_n}(k)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13451}%
|
|
$1/4$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13029}%
|
|
\begin{displaymath}
|
|
{D_N}(k) \approx {
|
|
{N \sin(\pi k) } \over {\pi k}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13453}%
|
|
$k = 3/2, 5/2, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13030}%
|
|
\begin{displaymath}
|
|
{2 \over {3 \pi}} \approx -13 \mathrm{dB} , \;
|
|
{2 \over {5 \pi}} \approx -18 \mathrm{dB} , \;
|
|
{2 \over {7 \pi}} \approx -21 \mathrm{dB} , \;
|
|
{2 \over {9 \pi}} \approx -23 \mathrm{dB} ,
|
|
\ldots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13031}%
|
|
\begin{displaymath}
|
|
{2 \over {5 \pi}} - {1\over 2} [ {2 \over {3 \pi}} + {2 \over {7 \pi}} ]
|
|
\approx -32.30 \mathrm{dB}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13457}%
|
|
$-42$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13459}%
|
|
$-49$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13461}%
|
|
$-54$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13463}%
|
|
$-59$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12556}%
|
|
\begin{figure}\psfig{file=figs/fig09.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13481}%
|
|
$k\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12563}%
|
|
\begin{figure}\psfig{file=figs/fig09.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13487}%
|
|
$k = 0, 1, \ldots, N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13493}%
|
|
$m = \ldots, 0, 1, \ldots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13499}%
|
|
$mH$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13505}%
|
|
$mH+n$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13032}%
|
|
\begin{displaymath}
|
|
S[m, k] = {\cal FT}\{w(n)X[n-mH]\} (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13033}%
|
|
\begin{displaymath}
|
|
S[k] = S[m, k]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13034}%
|
|
\begin{displaymath}
|
|
C[m] = S[m, k]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13533}%
|
|
$H=N/4$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13535}%
|
|
$FT$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13537}%
|
|
$3/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12577}%
|
|
\begin{figure}\psfig{file=figs/fig09.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13539}%
|
|
$C[m]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13541}%
|
|
$g[m]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13543}%
|
|
$g[m]C[m]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13549}%
|
|
$C[m-1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13551}%
|
|
$C[m-2]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13553}%
|
|
$|C[m]|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13565}%
|
|
$g[m, k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13567}%
|
|
$S[m, k] = C[m]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13035}%
|
|
\begin{displaymath}
|
|
g[m, k] =
|
|
\left \{
|
|
\begin{array}{ll}
|
|
{1 - f[k]/|S[m, k]|} & {|S[m, k]| > f[k]} \\
|
|
0 & \mbox{otherwise}
|
|
\end{array}
|
|
\right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13571}%
|
|
$f[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13577}%
|
|
$|S[m, k]|-f[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13579}%
|
|
$x = |S[m, k]|/f[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13581}%
|
|
$g(x) = 1-1/x$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13583}%
|
|
$x<1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12596}%
|
|
\begin{figure}\psfig{file=figs/fig09.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13589}%
|
|
$|S[m, k]|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13591}%
|
|
$|T[m, k]|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13036}%
|
|
\begin{displaymath}
|
|
g[m, k] = {{|T[m, k]|}\over{|S[m, k]|}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12610}%
|
|
\begin{figure}\psfig{file=figs/fig09.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13593}%
|
|
$\alpha = 3\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13595}%
|
|
$k=3$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13037}%
|
|
\begin{displaymath}
|
|
\begin{array}{lll}
|
|
{\angle S[0, 2] = \phi + \pi} &
|
|
{\angle S[0, 3] = \phi} &
|
|
{\angle S[0, 4] = \phi + \pi}\\
|
|
{\angle S[1, 2] = \phi + H\alpha + \pi } &
|
|
{\angle S[1, 3] = \phi + H\alpha} &
|
|
{\angle S[1, 4] = \phi + H\alpha + \pi}\\
|
|
{\angle S[2, 2] = \phi + 2H\alpha + \pi } &
|
|
{\angle S[2, 3] = \phi + 2H\alpha} &
|
|
{\angle S[2, 4] = \phi + 2H\alpha + \pi}\\
|
|
\end{array}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13601}%
|
|
$H\alpha$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13038}%
|
|
\begin{displaymath}
|
|
H \alpha = \angle S[1, 3] - \angle S[0, 3]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13039}%
|
|
\begin{displaymath}
|
|
\alpha = {{\angle S[1, 3] - \angle S[0, 3] + 2 p \pi} \over H}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13607}%
|
|
$2\pi/H$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13611}%
|
|
$8\pi/N = 4 \omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13623}%
|
|
$m-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12629}%
|
|
\begin{figure}\psfig{file=figs/fig09.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12634}%
|
|
\begin{figure}\psfig{file=figs/fig09.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13040}%
|
|
\begin{displaymath}
|
|
T[k] = {\cal FT}(W(n)X[n]) (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13041}%
|
|
\begin{displaymath}
|
|
T'[k] = {\cal FT}(W(n)X[n+H]) (k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13042}%
|
|
\begin{displaymath}
|
|
\angle S[m, k] = \angle S[m-1, k] +
|
|
\left ( \angle T'[k] - \angle T[k] \right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13043}%
|
|
\begin{displaymath}
|
|
= \angle \left (
|
|
{{S[m-1, k] T'[k]}
|
|
\over
|
|
{T[k]}}
|
|
\right )
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13044}%
|
|
\begin{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]}}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13651}%
|
|
$a = |T'[k]|$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13045}%
|
|
\begin{displaymath}
|
|
S[m, k] \; = \;
|
|
{
|
|
{ \left |
|
|
{{S[m-1, k]}
|
|
\over
|
|
{T[k]}}
|
|
\right |}
|
|
^
|
|
{-1}
|
|
}
|
|
\; \cdot \;
|
|
{
|
|
{{S[m-1, k] T'[k]}
|
|
\over
|
|
{T[k]}}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13657}%
|
|
$S[m,k+1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13659}%
|
|
$T'[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13661}%
|
|
$T'[k+1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13665}%
|
|
$S[m-1,k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13669}%
|
|
$T[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13671}%
|
|
$2N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13046}%
|
|
\begin{displaymath}
|
|
\angle T[k+1] - \angle T[k] = \angle S[m-1, k+1] - \angle S[m-1, k]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13047}%
|
|
\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}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13679}%
|
|
$S/T$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13048}%
|
|
\begin{displaymath}
|
|
S[m, k] \; = \;
|
|
{
|
|
{ \left |
|
|
R[k]
|
|
\right |}
|
|
^
|
|
{-1}
|
|
}
|
|
\cdot
|
|
{
|
|
{R[k] T'[k]}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13049}%
|
|
\begin{displaymath}
|
|
R[k] \; = \;
|
|
{
|
|
{
|
|
\overline {T[k]} \; \cdot \; {S[m-1, k]}
|
|
} \over {
|
|
\left |
|
|
{S[m-1, k]}
|
|
\right |
|
|
}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13685}%
|
|
$R[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13050}%
|
|
\begin{displaymath}
|
|
S[m, k] \; = \;
|
|
{
|
|
{ \left |
|
|
R'[k]
|
|
\right |}
|
|
^
|
|
{-1}
|
|
}
|
|
\; \cdot \;
|
|
{
|
|
{R'[k] T'[k]}
|
|
}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13051}%
|
|
\begin{displaymath}
|
|
R'[k] = R[k+1] + R[k] + R[k-1]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13052}%
|
|
\begin{displaymath}
|
|
R'[k+1] = R[k+2] + R[k+1] + R[k]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13695}%
|
|
$R'$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13703}%
|
|
$T'$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12678}%
|
|
\begin{figure}\psfig{file=figs/fig09.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13711}%
|
|
$(-1)^k$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13713}%
|
|
$\mathrm{fft}\sim$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12688}%
|
|
\begin{figure}\psfig{file=figs/fig09.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14083}%
|
|
\fbox{\texttt{fft\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14085}%
|
|
\fbox{$\mathrm{fft}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14093}%
|
|
\fbox{\texttt{rfft\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14095}%
|
|
\fbox{$\mathrm{rfft}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13723}%
|
|
$N/2+1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14099}%
|
|
\fbox{\texttt{tabreceive\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14101}%
|
|
\fbox{$\mathrm{tabreceive}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12705}%
|
|
\begin{figure}\psfig{file=figs/fig09.15.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14115}%
|
|
\fbox{\texttt{rifft\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14117}%
|
|
\fbox{$\mathrm{rifft}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13735}%
|
|
$N=512$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12717}%
|
|
\begin{figure}\psfig{file=figs/fig09.16.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13739}%
|
|
$s[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13743}%
|
|
$m[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath13053}%
|
|
\begin{displaymath}
|
|
\left \{
|
|
\begin{array}{ll}
|
|
{\sqrt{{s[k]-m[k]}\over {s[k]}}} & {s[k] > m[k]} \\
|
|
0 & \mbox{otherwise}
|
|
\end{array}
|
|
\right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14143}%
|
|
\fbox{\texttt{bang\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14145}%
|
|
\fbox{$\mathrm{bang}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14149}%
|
|
\fbox{\texttt{tabsend\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14151}%
|
|
\fbox{$\mathrm{tabsend}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13761}%
|
|
$1, 1/2, 1/3, \ldots, 1/b$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12740}%
|
|
\begin{figure}\psfig{file=figs/fig09.17.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13771}%
|
|
$c[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13773}%
|
|
$1/f[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13779}%
|
|
$c[k]/f[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure12748}%
|
|
\begin{figure}\psfig{file=figs/fig09.18.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14183}%
|
|
\fbox{\texttt{lrshift\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14185}%
|
|
\fbox{$\mathrm{lrshift}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14189}%
|
|
\fbox{\texttt{q8\_rsqrt\~}}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14191}%
|
|
\fbox{$\mathrm{q8\_rsqrt}\sim$}%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13799}%
|
|
$R'[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13829}%
|
|
$n=N/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13839}%
|
|
$2.5\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline13843}%
|
|
$k=2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{chapter}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14230}%
|
|
\begin{figure}\psfig{file=figs/fig10.01.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14745}%
|
|
$N/R$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14757}%
|
|
$A[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14633}%
|
|
\begin{displaymath}
|
|
X[n] = A[0] + A[1]{U^n} + \cdots + A[N-1]{U^{(N-1)n}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14634}%
|
|
\begin{displaymath}
|
|
X[n] =
|
|
A[0] + A[1](\cos(\omega n) + i \sin(\omega n)) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14635}%
|
|
\begin{displaymath}
|
|
+ A[N-1](\cos(\omega (N-1) n) + i \sin(\omega (N-1) n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14765}%
|
|
${U^{N/2}} = -1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14637}%
|
|
\begin{displaymath}
|
|
X[n+N/2] = A[0] - A[1]{U^n} + A[2]{U^{2n}} \pm \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14638}%
|
|
\begin{displaymath}
|
|
+ A[N-2]{U^{(N-2)n}} - A[N-1]{U^{(N-1)n}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14767}%
|
|
$X'$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14639}%
|
|
\begin{displaymath}
|
|
X'[n] = {{X[n] + X[n+N/2]}\over 2} =
|
|
A[0] + A[2]{U^{2n}} + \cdots + A[N-2]{U^{(N-2)n}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14769}%
|
|
$X''$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14640}%
|
|
\begin{displaymath}
|
|
X''[n] = {{X[n] - X[n+N/2]}\over 2} =
|
|
A[1]{U^n} + A[3]{U^{3n}} + \cdots + A[N-1]{U^{(N-1)n}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14777}%
|
|
$X[n] = X[n+N/2]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14783}%
|
|
$X'[n] = X[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14785}%
|
|
$X''[n] = 0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14791}%
|
|
$N/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14795}%
|
|
$X[n] = -X[n+N/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14801}%
|
|
$X[-n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14807}%
|
|
$X[N-n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14641}%
|
|
\begin{displaymath}
|
|
X[-n] =
|
|
A[0] + A[1](\cos(\omega n) - i \sin(\omega n)) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14642}%
|
|
\begin{displaymath}
|
|
+ A[N-1](\cos(\omega (N-1) n) - i \sin(\omega (N-1) n))
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14809}%
|
|
$X'[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14643}%
|
|
\begin{displaymath}
|
|
X'[n] = {{X[n] + X[-n]}\over 2} =
|
|
A[0] + A[1]\cos(\omega n)+ \cdots + A[N-1]\cos(\omega (N-1) n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14811}%
|
|
$X''[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14644}%
|
|
\begin{displaymath}
|
|
X''[n] = {{X[n] - X[-n]}\over {2i}} =
|
|
A[1]\sin(\omega n)+ \cdots + A[N-1]\sin(\omega (N-1) n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14817}%
|
|
$X[-n] = X[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14819}%
|
|
$X[-n] = -X[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14263}%
|
|
\begin{figure}\psfig{file=figs/fig10.02.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14829}%
|
|
${L_1}, \ldots, {L_j}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14833}%
|
|
${d_1}, \ldots, {d_j}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14835}%
|
|
$d_1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14837}%
|
|
${L_1}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14280}%
|
|
\begin{figure}\psfig{file=figs/fig10.03.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14841}%
|
|
$({L_1}, {d_1}) = (0.3N, -0.3)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14843}%
|
|
$({L_2}, {d_2}) = (0.6N, 1.3)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14645}%
|
|
\begin{displaymath}
|
|
s[n] = n/N - 1/2
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14845}%
|
|
$0 \le n \le N-1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14849}%
|
|
$(L, d)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14851}%
|
|
$s'[n] = d s[n-L]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14646}%
|
|
\begin{displaymath}
|
|
x[n] = {d_1} s[n - {L_1}] + \cdots + {d_j} s[n - {L_j}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14647}%
|
|
\begin{displaymath}
|
|
-{{{d_1} + \cdots + {d_j}} \over {N}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14853}%
|
|
${d_1} + \cdots + {d_j} = 0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14299}%
|
|
\begin{figure}\psfig{file=figs/fig10.04.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14648}%
|
|
\begin{displaymath}
|
|
p[n] = {1 \over 2} {{({n\over N} - {1\over 2})}^2} - {1 \over {24}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14861}%
|
|
$-1/N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14863}%
|
|
${M_i}, \ldots, {M_l}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14865}%
|
|
${c_1}, \ldots, {c_l}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14649}%
|
|
\begin{displaymath}
|
|
x[n] = {-N c_1} p[n - {M_1}] - \cdots - {N c_l} p[n - {M_l}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14318}%
|
|
\begin{figure}\psfig{file=figs/fig10.05.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14869}%
|
|
$n^2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14873}%
|
|
${c_1} + \cdots + {c_l} = 0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14650}%
|
|
\begin{displaymath}
|
|
A[k] = {1 \over N} {\cal FT}\{X[n]\}(k)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14651}%
|
|
\begin{displaymath}
|
|
= {1 \over N} \left [ X[0] +
|
|
{U^{-k}} X[1] + \cdots +
|
|
{U^{-(N-1)k}} X[N-1] \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14881}%
|
|
$x[n] - x[n-1]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14889}%
|
|
$k/N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14652}%
|
|
\begin{displaymath}
|
|
{\cal FT}\{ x[n-1] \} =
|
|
\left [ \cos(k \omega) - i \sin (k \omega) \right ]
|
|
{\cal FT}\{ x[n] \}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14653}%
|
|
\begin{displaymath}
|
|
\approx (1 - i \omega k) {\cal FT}\{ x[n] \}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14895}%
|
|
$k \omega = 2\pi k / N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14654}%
|
|
\begin{displaymath}
|
|
\cos(k \omega) \approx 1 \; , \; \sin(k \omega) \approx k \omega
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14897}%
|
|
$(k/N)^2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14655}%
|
|
\begin{displaymath}
|
|
{\cal FT}\{ x[n] - x[n-1] \} \approx i \omega k {\cal FT}\{ x[n] \}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14899}%
|
|
$s[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14901}%
|
|
$0 \le n < N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14656}%
|
|
\begin{displaymath}
|
|
s[n] - s[n-1] = -{1 \over N} +
|
|
\left \{
|
|
\begin{array}{ll}
|
|
{1} & {n = 0} \\
|
|
0 & \mbox{otherwise}
|
|
\end{array}
|
|
\right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14903}%
|
|
$-{1 \over N}$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14657}%
|
|
\begin{displaymath}
|
|
{\cal FT}\{ s[n] - s[n-1] \} (k) = 1 , \; k \neq 0, \; -N < k < N\
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14658}%
|
|
\begin{displaymath}
|
|
{\cal FT}\{ s[n] \} (k) \approx {1 \over {i \omega k}}
|
|
= {{-iN} \over {2 \pi k}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14909}%
|
|
$k \neq 0$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14913}%
|
|
$1/i = -i$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14915}%
|
|
${\cal FT}\{ s[n] \}(0)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14921}%
|
|
$k = \pm 1$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14659}%
|
|
\begin{displaymath}
|
|
{1 \over N}\left [
|
|
{\cal FT}\{ s[n] \} (1) \cdot {U^n} +
|
|
{\cal FT}\{ s[n] \} (-1) \cdot {U^{-n}}
|
|
\right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14660}%
|
|
\begin{displaymath}
|
|
\approx {{-i} \over {2 \pi}} \left [ U^n - U^{-n} \right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14661}%
|
|
\begin{displaymath}
|
|
= {{\sin ( \omega n)} \over {\pi}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14662}%
|
|
\begin{displaymath}
|
|
{{\sin ( k \omega n)} \over {k \pi}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14663}%
|
|
\begin{displaymath}
|
|
s[n] \approx {1 \over \pi} \left [
|
|
{\sin ( \omega n )}
|
|
+ {{\sin ( 2 \omega n)} \over 2}
|
|
+ {{\sin ( 3 \omega n)} \over 3}
|
|
+ \cdots
|
|
\right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14664}%
|
|
\begin{displaymath}
|
|
p[n] - p[n-1] = {
|
|
{
|
|
{{({n\over N} - {1\over 2})}^2} -
|
|
{{({{n-1}\over N} - {1\over 2})}^2}
|
|
} \over {
|
|
2
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14665}%
|
|
\begin{displaymath}
|
|
= {
|
|
{
|
|
{{({n\over N} - {N\over {2N}})}^2} -
|
|
{{({{n}\over N} - {{N - 2}\over {2N}})}^2}
|
|
} \over {
|
|
2
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14666}%
|
|
\begin{displaymath}
|
|
= {
|
|
{
|
|
{{{2n}\over {N^2}} - {1\over {N}}} + {1\over {N^2}}
|
|
} \over {
|
|
2
|
|
}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14667}%
|
|
\begin{displaymath}
|
|
\approx - s[n] / N .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14668}%
|
|
\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}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14669}%
|
|
\begin{displaymath}
|
|
\approx {{-1} \over N} \cdot {{-iN} \over {2 \pi k}}
|
|
\cdot {{-iN} \over {2 \pi k}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14670}%
|
|
\begin{displaymath}
|
|
= {N \over {4 {\pi ^2} {k^2}}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14671}%
|
|
\begin{displaymath}
|
|
p[n] \approx {1 \over {2 {\pi^2}}} \left [
|
|
{\cos ( \omega n )}
|
|
+ {{\cos ( 2 \omega n)} \over 4}
|
|
+ {{\cos ( 3 \omega n)} \over 9}
|
|
+ \cdots
|
|
\right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14407}%
|
|
\begin{figure}\psfig{file=figs/fig10.06.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14672}%
|
|
\begin{displaymath}
|
|
x[n] = s[n] - s[n-{N \over 2}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14937}%
|
|
$0 <= n < N/2$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14673}%
|
|
\begin{displaymath}
|
|
x[n] \approx {1 \over \pi} \left [
|
|
{\sin ( \omega n )}
|
|
+ {{\sin ( 2 \omega n)} \over 2}
|
|
+ {{\sin ( 3 \omega n)} \over 3}
|
|
+ \cdots
|
|
\right .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14674}%
|
|
\begin{displaymath}
|
|
\left .
|
|
-{\sin ( \omega n )}
|
|
+ {{\sin ( 2 \omega n)} \over 2}
|
|
- {{\sin ( 3 \omega n)} \over 3}
|
|
\pm \cdots
|
|
\right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14675}%
|
|
\begin{displaymath}
|
|
= {2 \over \pi} \left [
|
|
{\sin ( \omega n )}
|
|
+ {{\sin ( 3 \omega n)} \over 3}
|
|
+ {{\sin ( 5 \omega n)} \over 5}
|
|
+ \cdots
|
|
\right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14676}%
|
|
\begin{displaymath}
|
|
x[n] = 8 p[n] - 8 p[n-{N \over 2}]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14677}%
|
|
\begin{displaymath}
|
|
x[n] \approx {8 \over {{\pi^2}}} \left [
|
|
{\cos ( \omega n )}
|
|
+ {{\cos ( 3 \omega n)} \over 9}
|
|
+ {{\cos ( 5 \omega n)} \over 25}
|
|
+ \cdots
|
|
\right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14432}%
|
|
\begin{figure}\psfig{file=figs/fig10.07.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14947}%
|
|
$(0,0)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14949}%
|
|
$1/M$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14951}%
|
|
$-2/(N-2M)$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14678}%
|
|
\begin{displaymath}
|
|
x[n] = {{N^2} \over {MN - 2{M^2}}} (p[n-M] - p[n+M])
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14953}%
|
|
$p[n]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14955}%
|
|
$p[n-(N-M)]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14957}%
|
|
$p[n+M]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14679}%
|
|
\begin{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 .
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14680}%
|
|
\begin{displaymath}
|
|
\left .
|
|
+ {{\cos ( 2 \omega (n-M)) - \cos ( 2 \omega (n+M))} \over 4}
|
|
+ \cdots
|
|
\right ]
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14681}%
|
|
\begin{displaymath}
|
|
\cos(a) - \cos(b) = 2 \sin({{b-a}\over 2}) \sin({{a+b}\over 2})
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14682}%
|
|
\begin{displaymath}
|
|
{\cos ( \omega (n-M))} - {\cos ( \omega (n+M))} =
|
|
2 \sin (2 \pi M / N) \sin ( \omega n)
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14683}%
|
|
\begin{displaymath}
|
|
x[n] = a[1] \sin(\omega n) + a[2] \sin(2 \omega n) + \cdots
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14684}%
|
|
\begin{displaymath}
|
|
a[k] = {1 \over {{\pi ^ 2} (M/N - 2{{(M/N)}^2})}}
|
|
\cdot {{\sin (2 \pi k M / N) } \over {k^2}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14969}%
|
|
$M/N$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmldisplayA{displaymath14685}%
|
|
\begin{displaymath}
|
|
k < {{1} \over {4 M/N}}
|
|
\end{displaymath}%
|
|
\lthtmldisplayZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14975}%
|
|
$\sin(\theta) \approx \theta$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14977}%
|
|
$a[k]$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14989}%
|
|
$k \approx 1/(4\cdot 0.03) \approx 8.5$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14997}%
|
|
$2M$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline14999}%
|
|
$N/4M$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15001}%
|
|
$N/2M$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15005}%
|
|
$N/2M \approx 1/17$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15007}%
|
|
$1/50$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15009}%
|
|
$16\cdot 44100 =
|
|
705600$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15011}%
|
|
$705600-20000=685600$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15013}%
|
|
$685600/440=1558$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14466}%
|
|
\begin{figure}\psfig{file=figs/fig10.08.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{subsection}
|
|
\stepcounter{subsection}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14476}%
|
|
\begin{figure}\psfig{file=figs/fig10.09.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15031}%
|
|
$12\omega$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14483}%
|
|
\begin{figure}\psfig{file=figs/fig10.10.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14488}%
|
|
\begin{figure}\psfig{file=figs/fig10.11.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15041}%
|
|
$1/b$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
\stepcounter{section}
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14496}%
|
|
\begin{figure}\psfig{file=figs/fig10.12.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14503}%
|
|
\begin{figure}\psfig{file=figs/fig10.13.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlfigureA{figure14510}%
|
|
\begin{figure}\psfig{file=figs/fig10.14.ps}
|
|
|
|
\end{figure}%
|
|
\lthtmlfigureZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
{\newpage\clearpage
|
|
\lthtmlinlinemathA{tex2html_wrap_inline15045}%
|
|
$1 + 1/9 + 1/25 + 1/49 + 1/81 + \cdots$%
|
|
\lthtmlinlinemathZ
|
|
\lthtmlcheckvsize\clearpage}
|
|
|
|
|
|
\end{document}
|
|
|