H(z) is the system function for a stable LTI system and is given by: (a...

H(z) is the system function for a stable LTI system and is given by:

(a) H(z) can be represented as a cascade of a minimum-phase system H_min(z) and a unity gain all-pass system H_ap(z). Determine a choice for H_min(z) and H_ap(z) and specify whether or not they are unique up to a scale factor.

(b) Is the minimum-phase system, H_min(z), an FIR system? Explain.

(c) Is the minimum-phase system, H_min(z), a generalized linear-phase system? If not, can H(z) be represented as a cascade of a generalized linear-phase system H_lin(z) and an all-pass system H_ap2(z)? If your answer is yes, determine H_lin(z) and H_ap2(z). If your answer is no, explain why such representation does not exist