Example #2: Ix(t) Ix(t)I (t)=eu(t) Real Rea>0 (t) dt tat dt 0 (s+a)t S十a)∞ S+ a This converges only if Resta)<0, i.e. Re(s)<-Re(a) X2(5) S+a, tels]<-efar Same as X1(s), but different ROC ROC Key point(and key difference from FT): Need both x(s) and roc to uniquely determine x(t). No such an issue for FT
Example #2: This converges only if Re(s+a) < 0, i.e. Re(s) < -Re(a) Key Point (and key difference from FT): Need both X(s) and ROC to uniquely determine x(t). No such an issue for FT
Graphical visualization of the roc Example #1 Example #2 X1(s) 9e{s}>-9e{a} s+a +a at rig signal a2(t)=-eatu(t)-left-sided signal ga 9 plane plane g
Graphical Visualization of the RO C Example #1 Example #2