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\pard File Name: 428ca2.mcd\par ECE 428 Computer Assignment #2\par Dr. 
James S. Kang, ECE Department, Cal Poly Pomona\par \par Suppose that a 
ractangular pulse x(t) with amplitude h, pulse width a{\dn  }is 
sampled\par uniformly at an interval of T{\dn s}.  Let the sampled 
signal be x(k).  Assume h = 1V,  \par a = [(1/4) + {\f1 e]} s where {
\f1 e} is a small positive number.\par \par (a) Find the Fourier 
transform X({\f1 w}) and plot X({\f1 w}), the magnitude response, the 
phase response as a function of frequency {\f1 w}.\par \pard \par 
\pard (b) Let Ts = 0.1s.  Find the discrete-time Fourier transform X1({
\f1 q}) and plot X1({\f1 q}){\dn ,} the magnitude \par response, and 
the phase response as a function of frequency {\f1 q} from 0 to 2{\f1 p}
.  \par \pard N1 = 100. n = 0, 1, 2, ....., 99.  Sample X1({\f1 q}) at {
\f1 q} = n2{\f1 p}/N and compare with (1/T{\dn s})X({\f1 w}) sampled 
at\par {\f1 w} = n2{\f1 p}/(NT{\dn s}).  \par \pard \par (c) Let Ts = 
0.01s.   Find the discrete-time Fourier transform X2({\f1 q}) and plot X2({
\f1 q}){\dn ,} the magnitude \par \pard response, and the phase 
response as a function of frequency {\f1 q} from 0 to 2{\f1 p}.  \par 
\pard N2 = 100. n = 0, 1, 2, ....., 99.  Sample X2({\f1 q}) at {\f1 q} 
= n2{\f1 p}/N and compare with (1/T{\dn s})X({\f1 w}) sampled at\par {
\f1 w} = n2{\f1 p}/(NT{\dn s}). \par \pard \par (d) Let Ts = 0.001s.   
Find the discrete-time Fourier transform X3({\f1 q}) and plot X3({\f1 q}){
\dn ,} the magnitude \par \pard response, and the phase response as a 
function of frequency {\f1 q} from 0 to 2{\f1 p}.  \par \pard N3 = 
1000. n = 0, 1, 2, ....., N3-1.  Sample X3({\f1 q}) at {\f1 q} = n2{\f1 p}
/N and compare with (1/T{\dn s})X({\f1 w}) sampled at {\f1 w} = n2{\f1 p}/(NT{
\dn s}). \par \pard \par (e) Calculate the samples of X3({\f1 q}) at {
\f1 q} = n2{\f1 p}/N, N3 = 1000, n = 0, 1, 2, ....., 999, using CFFT.  
Notice that the samples of X2({\f1 q}) at {\f1 q} = n2{\f1 p}/N, N = 
100, n = 0, 1, 2, ....., 99 are equal to N*CFFT(x3) where x3 is the 
sampled function of x(t).  }
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{0:sinc}NAME({0:x}NAME):{0:if}NAME({0:x}NAME÷0,1,({0:sin}NAME({0:\p}NAME*{0:x}NAME))/({0:\p}NAME*{0:x}NAME))
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