PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 559

P.5.19 The ZT of the right-sided sequence f(n) is given by

Fz

z

zz

()

.

()(.)









102

1 031 1 0 43

1

11

Use MATLAB to determine the sequence f(n) by a partial fraction expansion and

verify the result obtained.

P.5.20 Let the input sequence of an LTI system be given by f(n) = 2(1/6)n u(n) − u(n − 1)

and its output sequence by g(n) = (1/6)n u(n). Determine

a. The impulse response

b. The step response

c. The system difference equation

d. The system transfer function

e. The system realization (in terms of delays, adders, and multipliers)

P.5.21 A system consists of two cascaded subsystems with the following transfer

functions:

He

e

e

jW

jW

(^1) jW

1

1

()









and

He

e

ee

jW

jW

(^2) jW j W 2

05

105 05

()

.

..









Determine

a. The difference equation of each subsystem

b. The poles and zeros for each subsystem

c. The difference equation of the overall system

d. The poles and zeros of the overall system

e. The overall system transfer function

f. A system realization in terms of delays, adders, and multipliers

g. The ROC of each subsystem and overall system

P.5.22 Let the system transfer function of an LTI system be given by

Hz

z

zz

()

.

.









102

1 031 0 43

1

(^12)
Use MATLAB to obtain
a. the system impulse response h(n)
b. its partial fraction expansion of H(z)
c. a pole/zero plot of the transfer function H(z)