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\pard File Name: 428ca1.mcd\par ECE 428 Computer Assignment #1\par Dr. 
James S. Kang, ECE Department, Cal Poly, Pomona\par \par Suppose that 
a ractangular pulse train x(t) with amplitude h, pulse width a, period T{
\dn o }is sampled\par uniformly at an interval of T{\dn s}.  Let the 
sampled signal be x(k).  Assume h = 1V, To = 1s, \par a = [(1/4) + {\f1 e]} 
s where {\f1 e} is a small positive number.\par \par (a) Find the 
complex exponential Fourier coefficients X{\dn n} and plot X{\dn n,} 
the magnitude response,\par and the phase response as a function of 
frequency.  Create a table of X{\dn n} as a function of n.\par \par 
(b) Let Ts = 0.1s.  Find the discrete-time Fourier coefficients d1{\dn n} 
and plot d1{\dn n,} the magnitude \par response, and the phase 
response as a function of frequency.  \par \pard Create a table of d1{
\dn n} as a function of n and compare X{\dn n} and d1{\dn n}.\par 
\pard \par (c) Let Ts = 0.01s.  Find the discrete-time Fourier 
coefficients d2{\dn n} and plot d2{\dn n,} the magnitude \par 
response, and the phase response as a function of frequency.  \par 
\pard Create a table of d2{\dn n} as a function of n and compare X{\dn n} 
and d2{\dn n}.\par \par \pard \par (d) Let Ts = 0.001s.  Find the 
discrete-time Fourier coefficients d3{\dn n} and plot d3{\dn n,} the 
magnitude \par response, and the phase response as a function of 
frequency.  \par \pard Create a table of d3{\dn n} as a function of n 
and compare X{\dn n} and d3{\dn n}.\par \pard \par (e) Calculate d3{
\dn n} using FFT.  In Mathcad, the definition of the function CFFT is 
the same as\par the definition of d{\dn n}.  Compare the time to 
calculate d3{\dn n} using CFFT and without using CFFT.  }
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