Page 350 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS

Fig. 6-27

SIMULATION

6.43. Consider the RC low-pass filter shown in Fig. 6-28(a) with RC = 1

Construct a discrete-time filter such that
hd[n] = hc(t)l, =n~, = hc(nTS) (6.1 72)

where hc(t) is the impulse response of the RC filter, h,[n] is the impulse
response of the discrete-time filter, and T, is a positive number to be chosen as
part of the design procedures.
Plot the magnitude response I H,(o)) of the RC filter and the magnitude response
(HJwTJ of the discrete-time filter for T, = 1 and T, = 0.1.

The system function H,(s) of the RC filter is given by (Prob. 3.23)
1
HJs) = -
s+ 1
and the impulse response h$) is

hc(t) = e-'u(t)
By Eq. (6.172) the corresponding h,[nl is given by

h,[n] = e-ncu[n] = (e-")"u[d