Question

Assume amplitude a = 4

The input to an LTI system is shown in the graph below. Assume a = 4. X(t) 20 t @ by 0 Ingineering Given that the Laplace transform of the output is Y(s) = - (s + 3)(1 – e-45)2 s(s + 5)2 a) Find the transfer function of the system and the region of convergence for o = Re(s). H(s) = RoC: For regions of convergence, answer in interval notation e.g. (-INF, a),(a,b) or (b, INF). b) is the system BIBO stable for a causal input? ? - c) Find the impulse response of the system. h(t) = Part b will only be marked correct if the answers to part a are correct.

Answer 1

from the diagram, alt) = { urt) – ult-a)] - [ utf-a)-ult-2a3 ach, 21+) = [u(t) = 444-#1] - [ uit-u) - 417-8)] Apply Leaplane. Transform Xus) = (1 - 33-17 Xus) = ☆ finess) - - *18) = [ordsj . ...alt-to) G 41 Geo ? . cesto xus), ... 21) - hit] yet? : XLS? Hils). Yks). : 14 · YL) = *15)HIS): Band (5+3)(1-4)-1(1705+45) ... 5151 52 .. - S+3 1 -'. HIS) (5+5)2 Real (0) k * 155-5 o -3 . Roc: >-5

th HIS) = S+3 5+5 -2 . - (S+592 (5+5)2 (5+5)2 HIS) = 1 : 1. Sth (5+52 Apply IVT .. hut) = . 1) - estuut) ba) = (1) estuut) 57-5 .. et ea ex sta *?- teat ult) e esta? ::: 07-9 b) : U het) - hlo) = 11 to . hl =0 % gt y a stable shn.