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. The signal x[n] is stable and has the pole-zero diagram shown in figure.

(a) What is the region of convergence, 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

(e) What is x[0]?

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

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

Transcribed Image Text:

1.5 z-plane 1 0.5 Fr 米 1 1 4 2 -0.5 -1 -1.5 -1 1 Re(z) z-plane 0.5 () 1 1 4 2 -0.5 -1 1 Re(z) 2. * (2) uf Im(2)