Page 463 - Schaum's Outline of Theory and Problems of Signals and Systems

450 PROPERTIES OF LINEAR TIME-INVARIANT SYSTEMS TRANSFORMS [APP. B

anu[n] - 1 Z
6[n - m] -zPm, all z except 0 if m > 0, or 03 if m < 0

1-az-' =- , IzI > la1
z-a
1 Z
-anu[-n - 11- =- , Izl < lal
1-az-' z-a

(COS fl,n)u[n 1 - z2 - (cos 0,)z , lzl > 1

z2 - (2cos no)z + 1
(sin n,n)u[n] - (sin 0,)z , 121 > 1

z2 - (2cos Ro)z + 1
(rn cos R,n)u[n] - z2 - (r cos no)z Izl > r

z2 - (2r cos n,)z + r2 '
(rn sin fl,n)u[n] - (r sin 0,)z

Izl > r
~~-(2rcos~~)z+r~'

OsnsN-1- 1 -aNz-N
otherwise 1 - az-I 9 IzI>O

The Unilateral (or One-sided) z-Transform:

Some Special Properties:
Time-Shifting Property:

Initial value theorem: x[O] = lim X( z)
z-rm
Final value theorem: lim x[N] = lim (1 - z- ')X( z)
N-m z- 1