PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 519

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frequency W

frequency W

Phase of DFT[g(n)] versus W

Magnitude of DFT[g(n)] versus W

Linear convolution [g(n) = conv(f(n), h(n))] versus n

time index n

40

100

50

0

20

Amplitude

Magnitude

Angle in rad.

− 20

0

5

0

− 5

FIGURE 5.31

Plots of part a of g(n) and DFT[g(n)] by evaluating the linear convolution of Example 5.6.

ste m (n,g g n);h old o n; plo t(n,g g n); yla b e l(‘A m plitu d e’);

xlabel (‘time index n’)

title(‘ Circular convolution g(n)=ifft[DTF(f(n)*DTF(h(n)] vs. n’)

subplot (3,1,2)

DFT _ cir = fft(ggn,9);

stem(n,abs(DFT _ cir));hold on; plot(n,abs(DFT _ cir));

xlabel(‘frequency W’);

ylabel(‘Magnitude’);

title(‘Magnitude of DFT[g(n)] vs. W’)

subplot (3,1,3)

stem(n, angle(DFT _ cir));hold on; plot(n, angle(DFT _ cir));

xlabel(‘frequency W’);

title (‘Phase of DFT[g(n)] vs. W’);ylabel(‘Angle in rad.’)

figure(3)

error = gn-ggn;

bar(n,error); title(‘[Errors] vs. time index n’)

ylabel (‘Amplitude’)

xlabel (‘ time index n’)

The script fi le convolutions is executed and the results are indicated in Figures 5.31

through 5.33.