Consider the z-transform X(z) whose pole–zero plot is as shown in Figure P3.4. (a)...

Consider the z-transform X(z) whose pole–zero plot is as shown in Figure P3.4.

(a) Determine the ROC of X(z) if it is known that the Fourier transform exists. For this case, determine whether the corresponding sequence x[n] is right sided, left sided, or two sided.

(b) How many possible two-sided sequences have the pole–zero plot shown in Figure P3.4?

(c) Is it possible for the pole–zero plot in Figure P3.4 to be associated with a sequence that is both stable and causal? If so, give the appropriate ROC.