Properties of laplace Transforms Many parallel properties of the Ctft, but for Laplace transforms we need to determine implications for the roc For example Inear an1(t)+b2(t)aX1(s)+bX2 (s) ROC at least the intersection of ROCs of X(s)and X2(s) ROC can be bigger(due to pole-zero cancellation) E. g and a Then a.1(t)+bm2()=0→→X(s)=0 → RoC entire s- planeProperties of Laplace Transforms • For example: Lineari t y ROC at least the intersection of ROCs of X1( s) and X2 ( s) ROC can be bigger (due to pole-zero cancellation) • Many parallel properties of the CTFT, but for Laplace transforms we need to determine implications for the ROC ⇒ ROC entir e s-plane