Page 126 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 31 LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS

Table 3-1 Some Laplace Transforms Pairs

1 All s

cos wotu(t)

sin wotu(t

s+a
e-"' cos wotu(t) Re(s) > - Re(a)
(s+a12+w;

A. Linearity:
If

The set notation A I B means that set A contains set B, while A n B denotes the
intersection of sets A and B, that is, the set containing all elements in both A and B.
Thus, Eq. (3.15) indicates that the ROC of the resultant Laplace transform is at least as
large as the region in common between R, and R2. Usually we have simply R' = R, n R,.
This is illustrated in Fig. 3-4.