4.56. Consider the system shown in Fig. 4-10. (a) Find the system function H(z). (b) Find the difference equation relating the output y[n] and input x[n]. Ans. (a) H(z) = + 7 -1 1+a,z+azz-2 (b) y[n]+a, y[n − 1]+a₂y[n-2]= box[n] + b,x[n − 1] + b₂x[n-2] x[n] a₂ b₂ Z-' b₁ bo Σ Σ y[n] Fig. 4-10

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4.56. Consider the system shown in Fig. 4-10.
(a) Find the system function H(z).
(b) Find the difference equation relating the output y[n] and input x[n].
Ans. (a) H(z) =
+ 7
-1
1+a,z+azz-2
(b) y[n]+a, y[n − 1]+a₂y[n-2]= box[n] + b,x[n − 1] + b₂x[n-2]
x[n]
a₂
b₂
Z-'
b₁
bo
Σ
Σ
y[n]
Fig. 4-10
Transcribed Image Text:4.56. Consider the system shown in Fig. 4-10. (a) Find the system function H(z). (b) Find the difference equation relating the output y[n] and input x[n]. Ans. (a) H(z) = + 7 -1 1+a,z+azz-2 (b) y[n]+a, y[n − 1]+a₂y[n-2]= box[n] + b,x[n − 1] + b₂x[n-2] x[n] a₂ b₂ Z-' b₁ bo Σ Σ y[n] Fig. 4-10
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