Page 206 - Schaum's Outline of Theory and Problems of Signals and Systems

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

Taking the inverse z-transform of Y(z), we get

which is the same as Eq. (2.134).

Using the z-transform, redo Prob. 2.29.
(a) From Prob. 2.29(a), x[n] and h[n] are given by

x[n] = anu[n] h[n] = Pnu[n]
From Table 4-1
z
~[n] anu[n] H X(Z) = - Izl> la1
=
z-a

Then

Using partial-fraction expansion, we have

( a I P
=--
where C, = - C2 = -
=-
z-P,=, a-P z-a~=p a-p
Thus,
a 2 P z
y(z) = - - - - - lzl > max(a, p)
a-p 2-(Y a-p 2-p

and

which is the same as Eq. (2.135). When a = P,

Using partial-fraction expansion, we have

where

and