Consider the stable LTI system with system function The system function H(z) ca...

Consider the stable LTI system with system function

The system function H(z) can be factored such that

where H_min(z) is a minimum-phase system, and H_ap(z) is an all-pass system, i.e.,

Sketch the pole–zero diagrams for H_min(z) and H_ap(z). Be sure to label the positions of all the poles and zeros. Also, indicate the ROC for H_min(z) and H_ap(z).