Using MATLAB,
(a) Generate a pseudo-random sequence of 256 data points in a vector x, using the randn function which is built in to MATLAB.
(b) Find the DFT of that sequence of data and put it in a vector X.
(c) Set a vector Xlpf equal to X.
(d) Change all the values in Xlpf to zero except the first 8 points and the last 8 points.
(e) Take the real part of the inverse DFT of Xlpf and put it in a vector xlpf.
(f) Generate a set of 256 sample times t which begin with 0 and are uniformly separated by 1.
(g) Graph x and xlpf versus t on the same scale and compare. What kind of effect does this operation have on a set of data? Why is the output array called xlpf?
% Solution to exercise 45 in Sampling and the DFT
close all ;
x = randn(256,1) ; X = fft(x) ;
mask = [ones(8,1);zeros(240,1);ones(8,1)] ;
Xlpf = mask.*X ;
xlpf = real(ifft(Xlpf)) ;
t = [0:255]’ ;
p = xyplot({t,t},{x,xlpf},[0,256,-3,3],’\itt’,...
‘x({\itt}) and x_l_p_f({\itt})’,’Times’,18,...
‘Times’,14,”,’Times’,24,{’n’,’n’},{’c’,’c’},{’k’,’k’}) ;
set(p{1},’LineWidth’,0.5) ;
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