The construction of special coprime factorizations in discrete time

Given a rational, discrete-time transfer matrix, it is shown how to construct two special kinds of coprime factorizations for it-normalized and all-pass denominator. This is done in two ways. First, by carrying the existing continuous-time construction results to discrete-time via a bilinear transformation. This is shown to be messy and computationally burdensome. Second, direct constructions are derived in discrete time. The derivations point out interesting differences between discrete and continuous time for these constructions