PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

516 Practical MATLAB® Applications for Engineers

over the ranges 0 ≤ k ≤ 32 and 0 ≤ k ≤ 64.

MATLAB Solution

% Script file: DTFT _ DFT

k = linspace(0,16,32);

fn32 = cos(3*pi*k/16);

kk = linspace(0,16,64);

fn64 = cos(3*pi*kk/16);

DFT _ fn32 = fft(fn32);

DFT _ fn64 = fft(fn64);

DFT _ fn = fft(fn32,256);

W = 0:1:255;

figure(1)

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 29]);

figure(2)

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))

subplot (2,1,2)

plot (W,angle(DFT _ fn))

axis ([0 259 -4 4])

hold on

plot (WWW,angle(DFT _ fn64),’o’,WWW,angle(DFT _ fn64));

axis([0 259 -4 4])

ylabel(‘Phase angle’)

xlabel(‘Index k’)

The script fi le DTFT_DFT is executed and the results are indicated in Figures 5.29

and 5.30.