A bounded-input bounded-output stable discrete-time LTI system has impulse response h[n]...

A bounded-input bounded-output stable discrete-time LTI system has impulse response h[n] corresponding to a rational system function H(z) with the pole–zero diagram shown in Figure P5.42.

In addition, we know that

(a) Determine H(z) and its ROC.

(b) Consider a new system having an impulse response g[n] = h[n + n₀], where n₀ is an integer. Given that G(z)|_z=0 = 0, and determine the values of n₀ and g[0].

(c) A new system has an impulse response, f [n] = h[n] ∗ h[−n]. Determine F(z) and its ROC.

(d) Is there a right-sided signal e[n] such that e[n]∗h[n] = u[n], where u[n] is the unit-step sequence? If so, is e[n] causal?