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{SECT 0 {PARA 18 "" 0 "" {TEXT -1 16 "Model Wave Forms" }}{PARA 19 "" 
0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(pl
ots):" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 "exponential waveforms p
eriodic on [0,1]" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 59 "set the freque
ncy, it should be an integer for periodicity " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 11 "n := 2.14:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 182 "e
[n]  :=  unapply(exp(n*(2*Pi*I*t)),t):\ne[-n]  := unapply(exp(-n*(2*Pi
*I*t)),t):\ne[n](t)=evalc(Re(e[n](t)))+I*evalc(Im(e[n](t)));\ne[-n](t)
=evalc(Re(e[-n](t)))+I*evalc(Im(e[-n](t)));\n" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 104 "plot([Re(e[n](t)),Im(e[n](t))],t=0..1,axes=boxed);\n
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{TEXT -1 48 "sampling exponential waveforms periodic on [0,1]" }}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 21 "Fi
x the sampling rate" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "N := 32;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"#K" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 26 "make exponential waveform " }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 58 "n := 3;\ne[n]  :=  unapply(exp(n*(2*Pi*I*t)),t):\ne[n](t);\n\n
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"nG\"\"$" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$expG6#,$*(%\"IG\"\"\"%#PiGF)%\"tGF)\"\"'" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 19 "sample the waveform" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 107 "X := [seq(e[n](i/N),i=0..N-1)]:\nX := evalf(X);\nRX \+
:= [seq(Re(X[i]),i=1..N)];\nIX := [seq(Im(X[i]),i=1..N)];\n" }}{PARA 
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.1,color=green):\n\nRsampwaves := plot([seq([i/N,RX[i+1]],i=0..N-1)],
\n                   style=point,symbol=box,color=red):\nIsampwaves :=
 plot([seq([i/N,IX[i+1]],i=0..N-1)],\n                   style=point,s
ymbol=circle,color=green):\ndisplay(\{plot(0,t=0..1,color=black),\n   \+
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