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% MATLAB script for Illustrative Problem 6, Chapter 1 
echo on 
ts=0.2;                     % set parameters 
fs=1/ts; 
df=0.01; 
x=[zeros(1,10),[0:0.2:1],ones(1,9),[1:-0.2:0],zeros(1,10)]; 
[X,x,df1]=fftseq(x,ts,df);          % derive the FFT 
X1=X/fs;                                    % scaling 
f=[0:df1:df1*(length(x)-1)]-fs/2;           % frequency vector for FFT 
f1=[-2.5:0.001:2.5];                        % frequency vector for analytic approach 
y=4*(sinc(2*f1)).^2-(sinc(f1)).^2;          % exact Fourier transform 
pause % Press akey to see the plot of the Fourier Transform derived analytically. 
clf 
subplot(2,1,1) 
plot(f1,abs(y)); 
xlabel('Frequency') 
title('Magnitude-pectrum of x(t) derived analytically') 
pause % Press akey to see the plot of the Fourier Transform derived numerically. 
subplot(2,1,2) 
plot(f,fftshift(abs(X1))); 
xlabel('Frequency') 
title('Magnitude-pectrum of x(t) derived numerically')