Page 202 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 41 THE z-TRANSFORM AND DISCRETE-TIME LTI SYSTEMS

and so by definition (4.3) we obtain
137
x[n] = {O,T,~,E,. -. )

4.19. Using partial-fraction expansion, redo Prob. 4.18.
Z - Z 1
-
2
(a) X(z)=2~2-3~+1 2(z-l)(z-+) lzl< -
Using partial-fraction expansion, we have

where

and we get

Since the ROC of X(z) is lzl < i, x[n] is a left-sided sequence, and from Table 4-1 we
get
x[n] = -u[-n - I] + - I] = [(i)n I]u[-n - 11
-

which gives
x[n] = (..., 15,7,3,l,O)

Since the ROC of X(z) is lzl> 1, x[n] is a right-sided sequence, and from Table 4-1 we
get

x[n] = u[n] - (i)'u[n] = [I - (i)']u[n]
which gives

4.20. Find the inverse z-transform of

Using partial-fraction expansion, we have

where