Page 102 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 21 LINEAR TIME-INVARIANT SYSTEMS 91

2.28. The input x[n] and the impulse response h[n] of a discrete-time LTI system are given
by

(a) Compute the output y[n] by Eq. (2.35).
(b) Compute the output y[n] by Eq. (2.39).
(a) By Eq. (2.35) we have

Sequences x[k] and h[n - k] are shown in Fig. 2-20(a) for n < 0 and n > 0. From Fig.
2-20(a) we see that for n < 0, x[k] and h[n - k] do not overlap, while for n 2 0, they
overlap from k = 0 to k = n. Hence, for n < 0, y[n] = 0. For n r 0, we have

Changing the variable of summation k to m = n - k and using Eq. (1.901, we have

(a)
Fig. 2-20