$\%$ Program P$3\_1$

$\%$ Illustration of the Aliasing Effect

$\%$ in the Frequency Domain

clf;

t $=0$:$0\mathrm{.}005$:$10$;

xa $=2*$t$.*$exp$(-$t$)$;

subplot$(2,2,1)$

plot$($t$,$xa$)$;grid

xlabel$($Time$,$ msec$)$;ylabel$($Amplitude$)$;

title$($Continuous$-$time signal x$\_\{$a$\}($t$))$;

subplot$(2,2,2)$

wa $=0$:$10/511$:$10$;

ha $=$ freqs$(2,[121],$wa$)$;

plot$($wa$/(2*$pi$),$abs$($ha$))$;grid;

xlabel$($Frequency$,$ kHz$)$;ylabel$($Amplitude$)$;

title$(|$X$\_\{$a$\}($j$\backslash$Omega$)|)$;

axis$([05/$pi $02])$;

subplot$(2,2,3)$

T$=1$;

n $=0$:T:$10$;

xs $=2*$n$.*$exp$(-$n$)$;

k $=0$:length$($n$)-1$;

stem$($k$,$xs$)$;grid;

xlabel$($Time index n$)$;ylabel$($Amplitude$)$;

title$($Discrete$-$time signal x$[$n$])$;

subplot$(2,2,4)$

wd $=0$:pi$/255$:pi;

hd $=$ freqz$($xs$,1,$wd$)$;

plot$($wd$/($T$*$pi$),$ T$*$abs$($hd$))$;grid;

xlabel$($Frequency$,$ kHz$)$;ylabel$($Amplitude$)$;

title$(|$X$($e$^\{$j$\backslash$omega$\})|)$;

axis$([01/$T $02])$