Page 197 - Schaum's Outline of Theory and Problems of Signals and Systems

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

By the time-reversal property (4.23) we obtain

(e) From Eqs. (4.8) and (4.10)
Z
anu[n] - - Izl> la1
2-a
Again by the time-reversal property (4.23) we obtain

4.11. Verify the multiplication by n (or differentiation in z) property (4.24), that is,

From definition (4.3)

Differentiating both sides with respect to 2, we have

and

Thus, we conclude that

4.12. Find the z-transform of each of the following sequences:

(a) x[n] = nanu[n]
(b) x[n] = nan- lu[n]
(a) From Eqs. (4.8) and (4.10)
Z
anu[n] o - IzI > la1
z-a
Using the multiplication by n property (4.24), we get