H (z) is the system function for a stable LTI system and is given by:
H (z) =
(1 − 2z−1)(1 − 0.75z−1)/(z−1(1 − 0.5z−1) )
.
(a) H (z) can be represented as a cascade of a minimum-phase system Hmin1(z) and a
unity-gain all-pass system Hap(z), i. e.,
H (z) = Hmin1(z)Hap(z).
Determine a choice for Hmin1(z) and Hap(z) and specify whether or not they are unique
up to a scale factor.
(b) H (z) can be expressed as a cascade of a minimum-phase system Hmin2(z) and a generalized linear-phase FIR system Hlp(z):
H (z) = Hmin2(z)Hlp(z).
Determine a choice for Hmin2(z) and Hlp(z) and specify whether or not these are
unique up to a scale factor.