The signal y[n] is the output of an LTI system with impulse response h[n] for a given in...

The signal y[n] is the output of an LTI system with impulse response h[n] for a given input x[n]. Throughout the problem, assume that y[n] is stable and has a z-transform Y(z) with the pole–zero diagram shown in Figure P3.48-1. The signal x[n] is stable and has the pole–zero diagram shown in Figure P3.48-2.

(a) What is the ROC, Y(z)?

(b) Is y[n] left sided, right sided, or two sided?

(c) What is the ROC of X(z)?

(d) Is x[n] a causal sequence? That is, does x[n] = 0 for n < 0?

(e) What is x[0]?

(f) Draw the pole–zero plot of H(z), and specify its ROC.

(g) Is h[n] anticausal? That is, does h[n] = 0 for n > 0?