Page 151 - Schaum's Outline of Theory and Problems of Signals and Systems

LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS [CHAP. 3

By Eqs. (3.30) and (3.32) we have

Hence,

The ROC of X(s) is Rds) > -3. Thus, x(t) is a right-sided signal and from Table 3-1 we
obtain

Note that there is a simpler way of finding A, without resorting to differentiation. This is
shown as follows: First find c, and A, according to the regular procedure. Then substituting the
values of c, and A, into Eq. (3.84), we obtain

Setting s = 0 on both sides of the above expression, we have

from which we obtain A, =

3.20. Find the inverse Laplace transform of the following X(s):

2s+ 1
(a) X(s) = - Re(s) > -2
,
s+2

s3 + 2s' + 6
(c) X(S) = , Re(s) > 0
sz + 3s
2s + 1 2(s + 2) - 3 3
-
-
(a) X(s)= - =2- -
s + 2 s + 2 s+2
Since the ROC of X(s) is Re(s) > -2, x(t) is a right-sided signal and from Table 3-1 we
obtain