Page 127 - Schaum's Outline of Theory and Problems of Signals and Systems

LAPLACE TRANSFORM AND CONTINUOUS-TIME LTI SYSTEMS [CHAP.

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Fig. 3-4 ROC of a, X,(s) + a, X,(s).

B. Time Shifting:
If

) '-*X(S) ROC = R

then x(t - to) -e-"[)X ( s 1 R'=R (3.16)
Equation (3.16) indicates that the ROCs before and after the time-shift operation are the
same.

C. Shifting in the s-Domain:

If

then e+"x(t) -X(s - so) R' = R + Re(so) (3.17)

Equation (3.1 7) indicates that the ROC associated with X(s - so) is that of X(s) shifted
by Re(s,,). This is illustrated in Fig. 3-5.

D. Time Scaling:

I f

x(t) ++X(S) ROC = R

then x(at)- -X ( - R1=aR
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