Page 48 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 11 SIGNALS AND SYSTEMS

(b) By definitions (1.43) and (1.44)
-21n <0
u[n + 21 - u[n] =
otherwise
and x[n](u[n + 21 - u[n]) is sketched in Fig. 1-30(b).
(c) By definition (1.48)
n=l
x[n ]S[n - 11 =x[l]S[n - I] = S[n - 11 =

which is sketched in Fig. 1-30(c).

(4
Fig. 1-30

1-24 The unit step function u(t) can be defined as a generalized function by the following
relation:
m
+(t)u(t) dt = jw4(t) dt (1.98)
1- m 0
where &(t) is a testing function which is integrable over 0 < t < m. Using this
definition, show that

Rewriting Eq. (1.98) as