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R2653/writing/papers/ShannonAndBack/LaTeX/PrandoniVetterli09_Figures.tex
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\documentclass[12pt,fullpage]{article} %{styles/epfldspbook} %a4paper,
\usepackage{makeidx}
\usepackage{amsmath,amssymb,latexsym}
\usepackage{fleqn}
\usepackage[usenames]{color}
\usepackage{epsfig,graphpap,subfigure,afterpage,lscape}
\usepackage{pstricks,pst-node,pst-plot,pstricks-add,pst-3dplot}
\usepackage{graphicx}
\usepackage{rotating}
\usepackage{psDSP}
\renewcommand{\baselinestretch}{1.5}
\newcommand{\itempar}[1]{\par\vspace{1em}\noindent{\sffamily\bfseries #1}\hspace{1ex}}
\newcommand{\circonv}{\mbox{\,$\bigcirc$\hspace{-1.8ex}\scriptsize{N} \,}}
\newcommand{\Real}[1]{\mbox{Re\{$#1$\}}}
\newcommand{\Imag}[1]{\mbox{Im\{$#1$\}}}
\newcommand{\ztrans}{\mbox{$z$-transform}}
\newcommand{\expt}[1]{\mbox{E[$#1$]}}
\newcommand{\proba}[1]{\mbox{P[$#1$]}}
\newcommand{\rect}{{\mbox{rect\,}}}
\newcommand{\sinc}{{\mbox{sinc\,}}}
% main index entry
\newcommand{\mie}[1]{{\bf #1}}
\makeindex
\def\hyph{-\penalty0\hskip0pt\relax}
\begin{document}
\title{From Lagrange to Shannon$\ldots$ and Back:\\Another Look
at Sampling}
\author{Paolo Prandoni and Martin Vetterli}
\date{}
\maketitle
\newpage
\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\center
\psset{xunit=3cm, yunit=3cm}%
\begin{pspicture}(-1,-1)(1,1)%
\psaxes[axesstyle=frame,%
yAxis=false,%
ticks=none]%
(-1,-1)(1,1)
\uput[0](0.6,0){$x[n]$}
\uput[90](0,0.6){\sc sampling}
\uput[180](-0.6,0){$x(t)$}
\uput[270](0,-0.6){\sc interpolation}
\psarc[linewidth=3pt,linecolor=gray]{<-}(0,0){2.2cm}{10}{65}
\psarc[linewidth=3pt,linecolor=gray]{<-}(0,0){2.2cm}{115}{170}
\psarc[linewidth=3pt,linecolor=gray]{<-}(0,0){2.2cm}{190}{235}
\psarc[linewidth=3pt,linecolor=gray]{<-}(0,0){2.2cm}{305}{350}
\end{pspicture}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\center
\begin{psCTplot}[dy=0.5,height=6cm]{-2.5}{2.5}{-0.8}{1.6}
\psclip{\psframe(-2.5,-0.8)(2.5,1.6)}
\psCTplotFunction[linewidth=2pt,linecolor=SpringGreen]%
{x dup 1 add -1 div exch %
dup -2 div exch %
dup -1 add -3 div exch %
-2 add -4 div %
mul mul mul }
\psCTplotFunction[linewidth=2pt,linecolor=Cerulean]%
{x dup 2 add exch %
dup -1 div exch %
dup -1 add -2 div exch %
-2 add -3 div %
mul mul mul }
\psCTplotFunction[linewidth=2pt,linecolor=RedOrange]%
{x dup 2 add 2 div exch %
dup 1 add 1 div exch %
dup -1 add -1 div exch %
-2 add -2 div %
mul mul mul }
\psCTplotFunction[linewidth=2pt,linecolor=MidnightBlue]%
{x dup 2 add 3 div exch %
dup 1 add 2 div exch %
dup 1 div exch %
-2 add -1 div %
mul mul mul }
\psCTplotFunction[linewidth=2pt,linecolor=PineGreen]%
{x dup 2 add 4 div exch %
dup 1 add 3 div exch %
dup 2 div exch %
-1 add 1 div %
mul mul mul }
\endpsclip
\end{psCTplot}
\end{figure}
\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\center
\begin{psDTplot}[dx=1,dy=1,height=6cm,sidegap=0.9]{-2}{2}{-2}{3}
\psclip{\psframe(-2.9,-2)(2.9,3)}
%\psset{linestyle=dashed}
\psDTplotFunction[linewidth=0.5pt,linecolor=SpringGreen,nmin=-2.5,nmax=2.5]%
{x dup 1 add -1 div exch %
dup -2 div exch %
dup -1 add -3 div exch %
-2 add -4 div %
mul mul mul } %
\psDTplotFunction[linewidth=0.5pt,linecolor=Cerulean,nmin=-2.5,nmax=2.5]%
{x dup 2 add exch %
dup -1 div exch %
dup -1 add -2 div exch %
-2 add -3 div %
mul mul mul %
2 mul } %
\psDTplotFunction[linewidth=0.5pt,linecolor=RedOrange,nmin=-2.5,nmax=2.5]%
{x dup 2 add 2 div exch %
dup 1 add 1 div exch %
dup -1 add -1 div exch %
-2 add -2 div %
mul mul mul %
.7 mul} %
\psDTplotFunction[linewidth=0.5pt,linecolor=MidnightBlue,nmin=-2.5,nmax=2.5]%
{x dup 2 add 3 div exch %
dup 1 add 2 div exch %
dup 1 div exch %
-2 add -1 div %
mul mul mul %
2.4 mul } %
\psDTplotFunction[linewidth=0.5pt,linecolor=PineGreen,nmin=-2.5,nmax=2.5]%
{x dup 2 add 4 div exch %
dup 1 add 3 div exch %
dup 2 div exch %
-1 add 1 div %
mul mul mul %
-1.5 mul} %
\endpsclip
\psset{linestyle=solid}
\psDTplotFunction[linewidth=2pt,linecolor=Tan,tmin=-2,tmax=2]%
{x dup 1 add -1 div exch %
dup -2 div exch %
dup -1 add -3 div exch %
-2 add -4 div %
mul mul mul %
1 mul %
x dup 2 add exch %
dup -1 div exch %
dup -1 add -2 div exch %
-2 add -3 div %
mul mul mul %
2 mul %
x dup 2 add 2 div exch %
dup 1 add 1 div exch %
dup -1 add -1 div exch %
-2 add -2 div %
mul mul mul %
.7 mul %
x dup 2 add 3 div exch %
dup 1 add 2 div exch %
dup 1 div exch %
-2 add -1 div %
mul mul mul %
2.4 mul %
x dup 2 add 4 div exch %
dup 1 add 3 div exch %
dup 2 div exch %
-1 add 1 div %
mul mul mul %
-1.5 mul %
add add add add}
%\endpsclip
\psDTplotData{-2 1 -1 2 0 0.7 1 2.4 2 -1.5}
\end{psDTplot}
\end{figure}
\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\rectFun{dup -0.5 lt {pop 0} {0.5 gt { 0 } {1} ifelse } ifelse }
\def\triFun{dup dup -1 lt {pop pop 0} {1 gt { pop 0 } {abs 1 exch sub} ifelse } ifelse }
\def\cubFunA{abs dup 2 exp -2.25 mul exch 3 exp 1.25 mul 1 add add }
\def\cubFunB{abs dup dup 8 mul exch 2 exp -5 mul add exch 3 exp -4 add add -0.75 mul }
\def\cubFun{
dup dup dup dup %
-2 lt {pop pop pop pop 0} {
2 gt {pop pop pop 0 } {
-1 lt {pop \cubFunB } {
1 gt {\cubFunB }
{\cubFunA}
ifelse }%
ifelse }%
ifelse }%
ifelse }
\begin{figure}[t]
\center
\begin{psDTplot}[dx=1,dy=1,height=6cm,sidegap=0.3]{-2.6}{2.6}{-2}{3}
%\psset{linestyle=dashed}
\psset{linecolor=BurntOrange}
\psDTplotFunction[linewidth=0.5pt]{x -2 sub \rectFun 1 mul}
\psDTplotFunction[linewidth=0.5pt]{x -1 sub \rectFun 2 mul}
\psDTplotFunction[linewidth=0.5pt]{x \rectFun 0.7 mul}
\psDTplotFunction[linewidth=0.5pt]{x 1 sub \rectFun 2.4 mul}
\psDTplotFunction[linewidth=0.5pt]{x 2 sub \rectFun -1.5 mul}
\psset{linestyle=solid}
\psset{linecolor=Black}
\psline(-2.6, 0)(2.6, 0)
\psline[linewidth=2pt,linecolor=Tan](-2, 1)(-1.5, 1)(-1.5, 2)(-.5,2)(-.5,0.7)%
(0.5,0.7)(0.5,2.4)(1.5,2.4)(1.5,-1.5)(2,-1.5)
\psDTplotData{-2 1 -1 2 0 0.7 1 2.4 2 -1.5}
\end{psDTplot}
\end{figure}
\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\center
\begin{psDTplot}[dx=1,dy=1,height=6cm,sidegap=0.3]{-2.6}{2.6}{-2}{3}
%\psset{linestyle=dashed}
\psset{linecolor=OliveGreen}
\psDTplotFunction[linewidth=0.5pt]{x -2 sub \triFun 1 mul}
\psDTplotFunction[linewidth=0.5pt]{x -1 sub \triFun 2 mul}
\psDTplotFunction[linewidth=0.5pt]{x \triFun 0.7 mul}
\psDTplotFunction[linewidth=0.5pt]{x 1 sub \triFun 2.4 mul}
\psDTplotFunction[linewidth=0.5pt]{x 2 sub \triFun -1.5 mul}
\psset{linestyle=solid}
\psset{linecolor=Black}
\psline[linewidth=2pt,linecolor=Tan](-2, 1)(-1, 2)(0,0.7)(1,2.4)(2,-1.5)
\psDTplotData{-2 1 -1 2 0 0.7 1 2.4 2 -1.5}
\end{psDTplot}
\end{figure}
\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{figure}[t]
\center
\begin{psDTplot}[dx=1,dy=1,height=6cm,sidegap=0.3]{-2.6}{2.6}{-2}{3}
%\psset{linestyle=dashed}
\psset{linecolor=RoyalPurple}
\psDTplotFunction[linewidth=0.5pt]{x -2 sub \cubFun 1 mul}
\psDTplotFunction[linewidth=0.5pt]{x -1 sub \cubFun 2 mul}
\psDTplotFunction[linewidth=0.5pt]{x \cubFun 0.7 mul}
\psDTplotFunction[linewidth=0.5pt]{x 1 sub \cubFun 2.4 mul}
\psDTplotFunction[linewidth=0.5pt]{x 2 sub \cubFun -1.5 mul}
\psset{linestyle=solid}
\psset{linecolor=Black}
\psDTplotFunction[linewidth=2pt,linecolor=Tan,nmin=-2,nmax=2]{%
x -2 sub \cubFun 1 mul %
x -1 sub \cubFun 2 mul %
x \cubFun 0.7 mul %
x 1 sub \cubFun 2.4 mul %
x 2 sub \cubFun -1.5 mul %
add add add add}
\psDTplotData{-2 1 -1 2 0 0.7 1 2.4 2 -1.5}
\end{psDTplot}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\def\sincFun{x 3.14 mul dup RadtoDeg sin exch div}
\begin{figure}[t]
\center
\begin{psCTplot}[dy=0.5,dx=5,height=6cm]{-13}{13}{-0.3}{1.1}
\psCTplotFile[linecolor=Violet,linewidth=0.4pt]{sincapp.txt}
\psCTplotFunction[linecolor=Tan]{\sincFun}
\end{psCTplot}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
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