Many properties of a discrete-time sequence h[n] or an LTI system with impulse response h[n] can be discerned from a pole–zero plot of H(z). In this problem, we are concerned only with causal systems. Clearly describe the z-plane characteristic that corresponds to each of the following properties:
(a) Real-valued impulse response
(b) Finite impulse response
(c) h[n] = h[2α − n] where 2α is an integer
(d) Minimum phase
(e) All-pass.
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