Question

Laplace Transform

Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace Transform table 9.2 find the bilinear Laplace transform, F($) and sketch the region of convergence (ROC) in the s-plane showing all poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 4e-2tu(t) + 7u(-t) – 10e-10t u(-t). Find the Bilinear Laplace Transform of fa(t) and sketch the region of convergence in s-plane also showing all the poles. State the ROC as an inequality.

Answer 1

Cinen f(t) = 48 24 (4) + 29 ult) U(+) LI है Roc a Realls) > 0 -2.1 2.1 Real (3) > 2 e tult) Roc > (5+2) Real (s) ko 2.1 16-A) - 15 Real (3) co 20C ) 2.7 -22 29 ul-A) Roc cmire so -2 < Real (5) co Roc =) f(x) = 29 5 (5+2) at -2,20 are poles location at iw shaded region is the Roc.

+7ul-A) - 10 e lot LT ult) - L.T 4 e 2t Roe z) Re(s) > 2 (5+2) L.T ult) LT 3 L.T .7 Roc=) Re(s)<o 74(-A) 10 10 e lot ult) (5 +10) Role) Re(s) <-10 Fa(s) : 4 (5+2) uto io (5+10) -2, -10,20 pales ar 2

Roc Gen2tult) is Re(s)>2 Here 7ult) ROC in Re(s) co -10 e lot ult) Re(s) C-10 ROC exist. commen ROC So WO lett handed rignal is Remember: Roc handed. always Right handed segnal is ROC always right