Page 44 - Schaum's Outline of Theory and Problems of Signals and Systems

SIGNALS AND SYSTEMS

Then
N- 1
aS=a C an=a+aZ+a" +-. +aN
n=O
Subtracting Eq. (1.95) from Eq. (1.941, we obtain

Hence if a # 1, we have

If a = 1, then by Eq. (1.94)

(6) For la1 < 1, lim aN = 0. Then by Eq. (1.96) we obtain
N-m
m N- l
]-aN I
--
x an = lim x an = lim -
-
n-0 N-m n =O N I - 1-a
(c) Using Eq. (1.911, we obtain

(d) Taking the derivative of both sides of Eq. (1.91) with respect to a, we have

and

Hence,

1.20. Determine whether the following signals are energy signals, power signals, or neither.
(a) x(t)=e-"'u(t), a>O (b) x(t)=Acos(w,t+8)
(c) x(t) = tu(t) (dl x[n] = (- 0.5)"u[n]
(e) x[nl= u[nl (f x[n] = 2ej3"