PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

514 Practical MATLAB® Applications for Engineers

Example 5.3

Let the real sequence h(n) be given by its DTFT as follows:

He

jW ee e ejW jW jW jW

()

.. ....




0 007 0 034  0 04^234 0 04 0 03 0 009ee

eeee

jW

jW j W j W j W



 

5

1 2 63.. ..2 81 23 41 5 0 4

Create the script fi le DTFT_H that returns the magnitude and phase plots of the DTFT

of H(ejW) versus W, using 128 discrete points over the range 0 ≤ W ≤ 4 π.

MATLAB Solution

% Script file: DTFT _ H

P = [0.007 0.034 0.04 0.04 0.03 0.009];

Q = [1 2.63 2.81 1.5 0.4];

W = linspace(0,4*pi,128);

H = freqz(P,Q,W);

subplot (2,1,1)

plot(W,abs(H))

title (‘Magnitude of H[exp(jW)] vs. W’)

ylabel (‘Magnitude’);xlabel(‘frequency W’);

subplot (2,1,2)

plot(W,angle(H))

title(‘Phase of H[exp(jW)] vs. W’)

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

The script fi le DTFT_H is executed and the results are shown in Figure 5.28.

0246810

0

0.2

0.4

0.6

0.8

1

Magnitude

Phase in rad.

12 14

02468101214

− 4

− 2

0

2

4

frequency W

frequency W

Magnitude of H[exp(jW)] versus W

Phase of H[exp(jW)] versus W

FIGURE 5.28
Magnitude and phase plots of the DTFT of H(ejW) of Example 5.3.