In this problem, we demonstrate that, for a rational z-transform, a factor of the form (...

In this problem, we demonstrate that, for a rational z-transform, a factor of the form (z−z0) and a factor of the form contribute the same phase.

(a) Let H(z) = z − 1/a, where a is real and 0 < a < 1. Sketch the poles and zeros of the system, including an indication of those at z = ∞. Determine H(e^jω), the phase of the system.

(b) Let G(z) be specified such that it has poles at the conjugate-reciprocal locations of zeros of H(z) and zeros at the conjugate-reciprocal locations of poles of H(z), including those at zero and ∞. Sketch the pole–zero diagram of G(z). Determine G(e^jω), the phase of the system, and show that it is identical to H(e^jω).