Question

12 • 171 T- (6) Figure 1 (b) Consider the interconnection of the LTI systems shown in Figure 2 below. (1) Find the impulse response h[n] of the total system. (ii) Determine and sketch the total impulse response h[n] if ht[n]= 8[n-1], h2[n] = 3u[n+4], h3[n] = -3u[n-2], and he[n] = 8[n+4]. xin that the syn] - Paragraph -

Answer 1

hin) Giren @ . ditt \ 5 1cm) = S(n+t)+ Son)= S(n-1) hem = (n tv + 8(0) + 28(n-1) gen) = 2600+ 6(n) = {{ $ent) + s(m)-scov)]* [s(n+1)+ bc)+ 2 560_v] Yn) = 2 [S(+)$(n+1)] + 2 [Sc41) + Sm] + u&(nii)* 8(n=33+ S (n+D+ Em + SchlSCn)+ s(n) * 28(n-1) - Scn-1) *S(n+1) - 5 (n-1) +S(n) – S(n-1* NO 28177) yon) = 2 S(+2) + 2 Senty +48(n) + SCA+D+ 8661798(n-1) - sen -SC0-1) –25 -2) yon) = 2 82n+2)+ 3 500+1 +46(0) + 8(6+)-281n-2) 3 12 13 - 1 of 1 .. hen huln) huins sym 4h3(n) total impulse response og. hin) = Thicn) s4h2cm) + hicho y hecn] * hun) han) = hecret bacoy * hacv] + [hirms? hgcm)'t hulny]

hen) = [sen -14 3000+4) +8(n+q)]+[8(n-1) * -3 u(1-2)* 8cn tw} hen) = (56**3uch+8)] + [stnu) + -3un+2)] . h(n) = 3 A(n+) - 3 u(n+1) hin) = 3 [ucn+7) - uCn't1] ↑ homo 3 3 3 3 3 3 ----=> ni 3 2 4 6 5 .7