PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Fourier and Laplace 451

h(t) = x(t)

−1.5 0 1.5 t

input x(t)

output y(t)

x(t)

1

FIGURE 4.91

Block box system diagram of P.4.16.

R 1 = 1 Ω

R 2 = 1 Ω

C = 2 F

Vi(w) V 0 (w)

FIGURE 4.92

Circuit diagram of P.4.17.

P.4.17 Verify that the transfer function of the circuit diagram of Figure 4.92 is given by

Hw

Vw

Vw

jw

i jw

()

()

()

(/)

(/)





0 1

2

12

14









a. Obtain plots of mag[H(w)] versus w and angle[H(w)] versus w

b. Estimate the circuit bandwidth

c. Estimate the regions of nondistortion

P.4.18 Repeat problem P.4.17 for the RC network shown in Figure 4.93, where

Hw

Vw

Vw

jw jw

i jw jw

()

()

()

(.)(.)

()..





0

2

05 05

15 025



P.4.19 Verify that the transfer function of the RC network shown in Figure 4.94 is given

by

Hw

Vw

Vw

jw

i jw

()

()

()





0 21

22

Estimate its bandwidth and the regions of nondistortion.

P.4.20 Assuming that the input x(t) = cos(t) for the system diagram shown in Figure 4.91,

create a MATLAB script fi le that returns the following plots:

a. x(t) versus t

b. X(w) versus w

c. h(t) versus t

d. mag[H(w)] versus w