Consider the causal LTID system represented in block diagram shown in Fig. 5.19. (a) Determine the difference equation relating the output \(\boldsymbol{y}[\boldsymbol{n}]\) and input \(\boldsymbol{x}[\boldsymbol{n}]\) and (b) Is the system stable?

Figure 5.19

(a)
\[
y[n]-\frac{1}{4} y[n-1]+\frac{1}{64} y[n-2]=x[n]-5 x[n-1]+7 x[n-2]
\]
(b) The ROC includes unit circle and the poles of system function are within unit circle. Hence, the system is stable.

Transcribed Image Text:

x[n] 4 21 2-1 -5 7 y[n]