Page 203 - Schaum's Outline of Theory and Problems of Signals and Systems

192 THE z-TRANSFORM AND DISCRETE-TIME LTI SYSTEMS [CHAP. 4

Substituting these values into Eq. (4,831, we have

Setting z = 0 in the above expression, we have

Thus,

Since the ROC is lzl> 2, x[n] is a right-sided sequence, and from Table 4-1 we get

4.21. Find the inverse t-transform of

is
Note that X(Z) an improper rational function; thus, by long division, we have

Let

Then

where

Thus.

3 Z 1 2
and X(z)=2z+--- + -- 121 < 1
2 2-1 22-2
Since the ROC of X(z) is (z < 1, x[n] is a left-sided sequence, and from Table 4-1 we get
(
x[n] = 2S[n + 11 + iS[n] + u[-n - 11 - $2"u[-n - 1)
= 2S[n + 11 + $[n] + (1 - 2"-')u[-n - 11