Multi-Plet Two-Channel Perfect Reconstruction FIR and Causal Stable IIR Filter Banks

This paper proposes a new class of two-channel structural perfect reconstruction (PR) finite-impulse response / infinite-impulse response (FIR/IIR) filter banks (FBs) called the multi-plet FBs. It generalizes the structural PR FBs proposed by Phoong and the conventional triplet FB in that it employs multiple lifting steps similar to the conventional lifting structure. Apart from the important structural PR property, the multi-plet FB can be systematically designed to meet a given specification on the passband/stopband ripples and transition bandwidth: a low-order prototype PR FB with a much wider transition band is first designed using nonlinear optimization in order to obtain a symmetric frequency response and prescribed passband and stopband ripples. As only a few variables are required, its performances can easily be controlled. A subfilter is then designed using second-order cone programming (SOCP) so that the prototype FB can be warped by means of frequency transformation to meet the desired transition bandwidth, while preserving the PR condition, passband/stopband ripples and lifting structure of the prototype FB. The design procedure is very general and it applies to both linear-phase/low-delay FIR and IIR multi-plet FBs. By formulating the K-regularity conditions as a set of linear equality constraints on the subfilter coefficients, multi-plet-based wavelet bases can easily be designed under the SOCP framework. Design examples show that the proposed approach offers more flexibility in controlling the frequency characteristics of the PR FBs and lower design complexity than conventional methods