Question

- A causal system has input x[n] and output y[n]. Use the transfer function to determine the impulse response of this system. (a) x[n] = [[n]+} \n - 1]- 38[n – 20, x[n] = [[n] - [n – 1] (b) x[n] = (-3)" u[n], y[n] = 4(2)"u[n] – (7)" u[n]

Answer 1

| le) x(tm)= Sny+s(n)- S(--) x(n) → (z)→R x(n-1-) → X(zzo : R0270 1270 (n+n.) → (2) Fio ; RN리' Z - Fransform - | S(n) → 1 x(z) = 1+17 가 9 (n) = (n) - Str) Y12 = 사휴러 transfer fun.= H (2) = Y(z) 1 , 리 Hz) = I- 1 - 2 (17) () = 2 ) C Searnetwith can same (z+ 1) 2림) CSScanned with CamScanner stronme n ter

3) te () ) () () by comparing 0 - B - - H) [일) ) 의 [1] Ain) 등 (Yun-Jun) impulse response of the system = y(n)=h(n) | 9In- un)) run) CS$canned with CamScanner STAIN

| ⑥ x(n)= (-3)um) 지) = LANT - 시22 z+3 190) = "un) Sun) { seunho 에 2) 제 쭒 를 = (-1)-() (-2)(-12) = z2Z2] [2-2) (-1) 112132) (23) (-) transfer function- | Ylz) - 37 (23) 지 12-9)|2-13) 22 CS$canned with CamScanner en

Hiz)= 32(2+3) (2-2)/2-1/2) = 32 ſ 2+3 L 12-812-1911 by partial fraction 12-2)(2-4) (2-2) 12-119) by solving- - A + B B=- Hla) = 35 (Bizva] - = 102 12-2) 72 12-1191 Hla) si by inverse z transform hin) = 10 12}'un) -7 (4)'un) *nauin) impuke response of the system = y tn )= hin) pin) = 10(9)%u(n) – 7 (3mum) CE CSScanned with CamScanner