Jordan Representation of Perfect Reconstruction Filter Banks using Nilpotent Matrices

This paper contains the factorization of the polyphase matrix of finite impulse response perfect reconstruction filter banks into unimodular factors containing finite Jordan nilpotent structures and the associated transform matrices. An important contribution of the paper is the proposal of a systematic procedure for the construction of the transform matrices. The factorization is based on the M-channel lifting scheme which is essentially a prime factorization. It leads to simple implementation structures maintaining the computational complexity unchanged.