Question

5. Consider an LTI system with transfer function H(s). Pole-zero plot of H(s) is shown below. Im (a) How many ROCs can be considered for this system? (b) Assume system is causal. Find ROC of H(S) (c) Assume y(t) is system output with step unit as input. Given lim y(t) = 5 , 00 Find H(s).

Answer 1

-2 -1 of a) Roc must not contain any pole so there are only 2 ROC ROCA - Reds}{-2. Roc2 => Reds} yo 6) If systemis causal then Roc must be right sided and does not contain any pole so Roc: Reas}>o c) H(S) = K (st) (S-2 - K(5²1) SCSH)(3+2) SCSH)(3+2) Lim yet)=5 or to Lim Syco. suyo Lim K(941) (5) - K SO SCH) 6+2) - 225 kao SOHB) 10 (5²1) SCSH) (12)