Page 52 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 11 SIGNALS AND SYSTEMS

1.30. Evaluate the following integrals:

(d) /m e-'S(2t - 2) dt
- w

(a) By Eq. (1.21), with a = - 1 and b = 1, we have

(b) By Eq. (1.20, with a = 1 and b = 2, we have

(c) By Eq. (1.22)

=l +COST= 1 -1=0

(d) Using Eqs. (1.22) and (1.23), we have
m
-
1)]
/-Cts(2t - 2) dt = Irn dt
e-'S[2(t
-m

(el By Eq. (1.29)

1.31. Find and sketch the first derivatives of the following signals:
(a) x(t) = u(t) - u(t -a), a > 0
(b) ~(t) t[u(t) - u(t -a)], a > 0
=

(a) Using Eq. (1.301, we have

ul(t) = S(t) and ul(t -a) = S(t - a)