Question

Find the impulse response of the system shown in Figure 1. Assume that h(n) = h (n) = /1n un) h3(n) = u(n) 11n haln) = (3) "un) mon) - mm hi(n) h2(n) x(n) y(n) ☺ - Helm von h₃ (n) han) Figure 1. The system.

Answer 1

This question is related to the basics of z-transform. As system is cascade and combination of different systems, So you must analyse it accordingly which is shown in the solution steps by steps.

del - Rosco) dia Step. It converting this structure in z-domain wing 2-transform X(2) = noon no Banan Step2 Solve the transfer fun? Step 3 - Evaluate it to find impule reponic H(2) - (2) / 42) thy (2) f B YZ) = [112) Ha (2) - Hulz)] H3 (2) H, (2) Males thing anup 2 transform Tazt ; lal slal Hi(2) = Hale) = -!. as hulw) = bum) = (4) m) H (2) = 7-12 as h3 ) = Un) Hy (2) = 12 as huln) = (1) un

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esbon e for Impule response x(n) = S(n) .. xml= dom z tanform Yes = contaje (12) Cond) C1-92") Yes to be in the wing partial fraction (143)(1-7) ibble Febbe B = bin a (1. = lim 2 (1-21) = lein -1 (1-3152 (1-3) - lin -1 (1-z*j* [**] -1 (1-3)*(0) 08 A = lim cl-z) z d2 CH2 (1-²) 23

You a = lim El De lim 2 23 (Afr) (I) - (I- D | (112 (0-1) |- Yen=403) [ cerevo) - ] / 2 1-21 og veje ling inverte identitu Cat) anum) (1-92) 2 2 bangsom to Tot anum) impule response yon ) = 0.25 u(1) - (n+1) (3) Un) + (2) ucn)