Convolution Property h() +y(t)=b(t)米(t) Forx(t)←X(s),y(t)←→Y(s),b(t)←→H(s) Then Y(s)=H(s)·X(s) ROC of Y(s)=H(s)X(s: at least the overlap of the roCs of H(s)& X(s) ROC could be empty if there is no overlap between the two ROCs E. g x(t=eu(t and h(t)=-e u(t) ROC could be larger than the overlap of the two. e. g a()米b(t)=6(t)Convolution Property For Then • ROC of Y(s) = H(s)X(s): at least the overlap of the ROCs of H(s) & X(s) • ROC could be empty if there is no overlap between the two ROCs E.g. • ROC could be larger than the overlap of the two. E.g. x(t ) e u(t ), h(t ) e u( t ) t t = = − − − and