Question

(25) 15 points Find the discrete time impulse response of the following system if its Region of Convergence is } <=< 1 - 12- H(2) = (1 - 32-1) (1 - 12-1) (1- Lütfen birini seçin: k 1 1 1 a. u(-k – 1) k k 3 1 1 u(k) 2 u(k) 2 3 * (*) *u(6–1) +} (3) } (3) 1 (3) * (1) *ux) +; (3) *u-k – 1) k k 3 1 1 1 (19) u(-k – 1) u(k) 2 1 1 d.

Answer 1

Given H(-2) = 1-421 (-42') (1-1821) skept 19 H(2) (2 - 4) - 2 5 2 (2-4) 12-13) partial fractions step2. Taking z Vy (2-13) (2:13) - В 12-13 7.94 z(A+B). - ( 2 + 2 ) both sides comparing Coefficients A+B = -1 ☆ + B - Vy 2 A+ 3B. step solving and roxy. 4 AthB = 4 HA+B3 A+B=1 A 21-B 21-1-1/2) A 2 312 HA+G.B = -2Br 1 - B = -1/2

- H(2) 7 (kov ae-va 2(2-1/3) -- Z Holz) Formula -ROC ROO Xog) 2 polzi za Roce - ain) = -ahol-n-1) x(n) - anuch). ROC stepy: Given 1 1 241/2 ie and Izll/ (102). (thun) Uzen) -4° Ult-1) Hlza 3 steps odying inverse z-transform hin), ******-1) - Cor) hin) +