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H(z) =(1-3z^-1) / ( 2-z^-1)

(a) Sketch the pole-zero plot of H(z).

(b) Suppose the system is stable. Determine all possible regions of convergence (ROC) for H(z) under this condition, or state that none exists.

(c) Repeat part (b) assuming the system is causal instead of stable.

(d) Can this system have a causal and stable inverse? If so, determine

H^(-1)(z) including its ROC. If not, explain why not.