asmani
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Hi all
According to the textbook Signal and Systems by Oppenheim (2nd edition) pages 685 and 686, if the Laplace transform of x(t) is X(s) with ROC (region of convergence) R, then the Laplace transform of x(at) is (1/|a|)X(s/a) with ROC R/a.
Consequently, for a>1, there is a compression in the size of the ROC of X(s) by a factor 1/a.
But I think the ROC must be aR and not R/a, as the example x(t)=e-|t| shows. Which is correct?
Thanks
According to the textbook Signal and Systems by Oppenheim (2nd edition) pages 685 and 686, if the Laplace transform of x(t) is X(s) with ROC (region of convergence) R, then the Laplace transform of x(at) is (1/|a|)X(s/a) with ROC R/a.
Consequently, for a>1, there is a compression in the size of the ROC of X(s) by a factor 1/a.
But I think the ROC must be aR and not R/a, as the example x(t)=e-|t| shows. Which is correct?
Thanks