Page 142 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 31 LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS

3.6. Let

Find X(s) and sketch the zero-pole plot and the ROC for a > 0 and a < 0.
The signal x(t) is sketched in Figs. 3-12(a) and (b) for both a > 0 and a < 0. Since x(t) is
a two-sided signal, we can express it as
x(t) =e-"u(t) +ea'u(-r) (3.67)

Note that x(t) is continuous at t = 0 and x(O-) =x(O) =x(O+) = 1. From Table 3-1

1
earu( -t) H - - Re(s) <a (3.69)
s-a

(c)
Fig. 3-12