Consider the causal LTID system represented in block diagram shown in Fig. 5.19. (a) Determine the difference

Question:

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

image text in transcribed (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.