M-channel lifting-based design of paraunitary and biorthogonal filter banks with structural regularity

This paper presents a lifting-domain design of filter banks with a given McMillan degree. It is based on the M-channel lifting factorizations of the degree-0 and 1 building blocks I - 2uv^† and I - uv^† + z^-1uv^†, with v^†u = 1. Paraunitariness further requires u = v. The proposed lifting factorization has a unity diagonal scaling throughout, and guarantees perfect reconstruction (PR) even when the parameters are quantized. It is shown to be minimal in terms of the minimum number of delays required. Based on the lifting factorization, regularity of the FB can be structurally imposed, and reversible, possibly multiplierless, implementation of the FB can readily be derived. Design examples are given to illustrate the versatility of the proposed approach.