PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

506 Practical MATLAB® Applications for Engineers

− 4 − 3 − 2 − 1 0 1 2 3 4

0.5

1

1.5

2

2.5

DTFT [0.6n^ u(n)] = 1./(1-0.6*exp(-j.*W))

frequency W in rad.

− 4 − 3 − 2 −10 1 2 3 4

frequency W in rad.

Magnitude

− 1

−0.5

0

0.5

1

Phase in rad.

FIGURE 5.18
DTFT of f(n) of Example 5.1.

MATLAB Solution

% Script file : DTFT

% part(b)

W = linspace(-pi,pi,21);

DTFT = 1./(1-0.6*exp(-j.*W));

figure(1

subplot (2,1,1)

plot (W,abs(DTFT));title(‘ DTFT [0.6^n u(n)] = 1./(1-0.6*exp(-j.*W))’);

xlabel (‘frequency W in rad.’), ylabel(‘Magnitude’)

subplot (2,1,2)

plot (W,angle(DTFT));

xlabel (‘frequency W in rad.’), ylabel(‘Phase in rad.’)

figure(2)

% part(c)

P = [1 0]; Q = [1 -0.6];

h = freqz (P,Q,W);

subplot (2,1,1)

plot (W,abs(h));title(‘DTFT[0.6^n u(n)] using freqz’);

xlabel (‘frequency W in rad.’), ylabel (‘Magnitude’)

subplot (2,1,2)

plot (W,angle(h));

xlabel (‘frequency W in rad.’), ylabel (‘Phase in rad.’)

figure(3)

error _ mag=abs(DTFT)-abs(h);

error _ phase=angle(DTFT)-angle(h);

subplot(2,1,1);

bar(W,error _ mag);

title(‘Magnitude error’);ylabel(‘Amplitude’)

subplot(2,1,2);

bar(W,error _ phase);xlabel(‘frequency W in rad. ‘);

title(‘Phase error’), ylabel(‘Phase in rad.’);

The script fi le DTFT is executed and the results are shown in Figures 5.18 through 5.20.