Time Shift a(t-r)esX(s), same ROC as X(s) Exampl 3. +2 9e{}>-24 ST s+2 Re{s}>-24→c2u(t) t→→t-T ↓T=-3 3s s+2 e{s}>-2←c-2(+32(t+3)
Time Shift
Time-Domain Differentiation + dar( t + sX(se ds da sX(s); with ROC containing the ROC of X ( s) ROC could be bigger than the roc of X(s), if there is pole-zero cancellation. E. g 9te{s}>0 dt 8(t)+1=s. ROC= entire s-plane S-Domain Differentiation dx ta(t) ds, with same RoC as X(s)(Derivation is similar to d dt E te-(t ds s+ 9e{s}>-a S+a
Time-Domain Differentiation ROC could be bigger than the ROC of X( s), if there is pol e-zero cancellation. E.g., s -Domain Differentiation