Rational transfer matrices with FIR inverses

Abstract

We present a simple extension for rational transfer matrices of known results characterizing the invariant factors of causal FIR matrices with FIR inverses. This includes and generalizes previous characterizations of causal FIR multirate filter banks with anticausal FIR inverses, the so-called cafacafi systems. In particular, we extend (to the rational case) the result that G(z) is a square cafacafi system if and only if its determinantal degree is equal to its McMillan degree.