1、Chapter 9The Laplace Transform- ROC of LTReview:Denotation:Note:This transform is often called the bilateral Laplace transform, to distinguish it from the unilateral Laplace transform.The relationship between FT and LTReReS-planeS-planeImIm-a-aROC of Ex 9.1ROC of Ex 9.2 A convenient way to display t

2、he ROC is shown as the following figure:Rational Transforms Many (but by no means all) Laplace transforms of interest to us are rational functions of s (the preceding examples)N(s), D(s) polynomials in s Any x(t) consisting of a linear combination of complex exponentials for t0 and for t0 will also

3、in the ROC. Property5: If x(t) is left sided, and if the line Res=0 is in the ROC, then all values of s for which Res0 will also in the ROC. Property6: If x(t) is two sided, and if the line Res=0 is in the ROC, then the ROC will consist of a strip in the s-plane that includes the line Res=0 .Normall

4、y, RResL. (R0, the Laplace transform of x(t) is:ImRe-bbS-planeThe pole-zero plot isProperty7: If X(s) is rational, then its ROC is bounded by poles or extends to infinity. In addition, no poles of X(s) are contained in the ROC.Property8: Suppose X(s) is rational, then if x(t) is right sided, the ROC is to the right of the rightmost pole. If x(t) is left sided, the ROC is to the left of the leftmost pole.Example 9.8ImReS-planeImReS-planeImReS-planeImReS-pl