PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 521

Note that the error in the evaluation of g(n) performed by comparing the linear convo-

lution with respect to the circular convolution, is extremely small, in the order of 10−^15.

Example 5.7

Let

fn

n

n

n

()

016

116 32

033 64



    

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Create the script fi le rectang that returns the following plots:

a. f(n) versus n

b. The magnitude and phase plots of DFf T[f(n)] versus k, and compare it with the magni-

tude and phase plots of DFT[f(n)] versus k, over the ranges 0 ≤ k ≤ 32 and 0 ≤ k ≤ 64

MATLAB Solution

% Script file: rectang

k = linspace(0,63,64);

fn = [zeros(1,16) ones(1,16) zeros(1,32)];

DFT _ fn = fft(fn,256);

DFT _ fn64 = fft(fn,64);

DFT _ fn32 = fft(fn,32);

W=0:1:255;

figure(1)

plot (k,fn,‘o’,k,fn),axis([0 63 0 1.1]); title(‘ f(n) vs. t’)

xlabel (‘time index n’); ylabel(‘Amplitude’)

figure(2)

subplot (2,1,1)

plot (W,abs(DFT _ fn));

title(‘ Magnitudes of the DTFT and DFT’)

ylabel(‘Amplitude’)

%axis([0 259 0 20])

hold on

WW=linspace(0,255,32);

plot(WW,abs(DFT _ fn32),‘*’,WW,abs(DFT _ fn32))

axis([0 259 0 20])

subplot(2,1,2)

plot(W,abs(DFT _ fn));

ylabel(‘Amplitude’)

hold on

WWW= linspace(0,255,64);

plot(WWW,abs(DFT _ fn64),‘o’,WWW,abs(DFT _ fn64));

xlabel(‘ Index k’);axis([0 259 0 20]);

figure(3)

subplot(2,1,1)

plot(W,angle(DFT _ fn));

title(‘ Phase of the DTFT and DFT’)

ylabel(‘Phase angle’)

%axis([0 259 -4 4])

hold on

plot(WW,angle(DFT _ fn32),‘*’,WW,angle(DFT _ fn32))