Page 351 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS [CHAP. 6

(b)
Fig. 6-28 Simulation of an RC filter by the impulse invariance method.

Then, taking the z-transform of Eq. (6.175), the system function Hd(z) of the discrete-
time filter is given by
1
= , -e-Tsz-,

from which we obtain the difference equation describing the discrete-time filter as
y[n] - e-Tsy[n - 1) =x[n] (6.176)

from which the discrete-time filter that simulates the RC filter is shown in Fig. 6-28(b).
(b) By Eq. (5.40)

Then

By Eqs. (6.34) and (6.81)

From Eq. (6.149)