Page 124 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 31 LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS

(a) (b)
Fig. 3-2 ROC for Example 3.2.

Fig. 3-3 s-plane representation of X(s) = (2s + 4)/(s2 + 4s + 3).

Property 1: The ROC does not contain any poles.
r
Property 2: If x(t) is a finiteduration signal, that is, x(r) = 0 except in a finite interval r, 5 2 r,
(-m < I, and I, < m), then the ROC is the entire s-plane except possibly s = 0 or s = E.
Property 3: If x(t) is a right-sided signal, that is, x(r) = 0 for r < r, < m, then the ROC is of the form