PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

548 Practical MATLAB® Applications for Engineers

Error = [part(b)-part(c) versus n

6

8

× 10 −^16

4

2

0

− 2

− 4

− 6

− 5 051015 20 25 30 35

time index n

Amplitude

FIGURE 5.62
Time-domain error given by error = part b − part c of Example 5.14.

Example 5.15

Create the script fi le analys that analyzes the discrete system transfer function given by

He Ge

Fe

ee

ee

jW jW

jW

jW jW

() jW j W

()

()

.

..









509

107 03

2

2

and returns the following:

a. The pole/zero plot of H(ejW) (evaluates the system stability) (Figure 5.63)

b. The plot of abs{H(ejW)} versus W (Figure 5.64)

c. The plot of angle {H(ejW)} versus W

d. List all the poles, zeros, and stand alone term of the transfer function H(z=ejW) and

compare the results obtained with the results of part a

e. Determine the ROC of H(z = ejW)

f. The magnitude of the system poles (length from origin)

g. The partial fraction expansion of H(z)

h. h(n) by using the symbolic MATLAB inverse ZT of H(z)

MATLAB Solution

%Script file = analys

num = [5 0.9 1];

den = [1 -0.7 0.3];

figure(1)

zplane(num,den); title(‘Pole and zero plot of H(z)’)

figure(2)

W = -pi:pi/99:pi;

[H,W] = freqz(num,den,W);