Page 181 - Schaum's Outline of Theory and Problems of Signals and Systems

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

Thus,
6[n] H 1 all z

B. Unit Step Sequence dnl:

Setting a = 1 in Eqs. (4.8) to (4.101, we obtain

C. z-Transform Pairs:
The z-transforms of some common sequences are tabulated in Table 4-1.

Table 4-1. Some Common z-Transform Pairs

All z

lzl > 1

Izl< 1
Z-"' All z except 0 if (m > 0) or m if (m < 0)
1 Z
Izl > lal
1-az-''2-a

z2 - (COS no)z
(COS Ron)u[nl lzl> 1
z2 - (2cos Ro) t + 1
(sin no) z
(sin R,n)u[n] Izl> 1
z2 - (2cos R,)z + 1
z2 - (rcosR0)z
(rn cos R,n)u[n] Izl> r
z2 - (2r cos Ro)z + r2
(r sin R,)z
(rn sin R,n)u[nI Izl> r
z2 - (2r cos R,)z + r2

O<nsN-1
( otherwise 1 - ~"'z-~ lzl> 0
1 - az-'