The theory and design of recombination nonuniform filter-banks with linear-phase analysis/synthesis filters

This paper studies the theory and design of a class of linear-phase (LP) nonuniform filter-banks (FBs) called recombination nonuniform FBs (RNFBs). It is based on a recombination structure, where certain channels of an M-channel uniform FB are merged by synthesis filters of transmultiplexer (TMUX). It is assumed that the numbers of channels of the FB and TMUX are coprime to each other so that it is possible to obtain linear-time invariant (LTI) analysis/synthesis filters, instead of linear periodic time varying (LPTV) filters. The spectral supports of the analysis filters are analyzed, and the existence and matching conditions to obtain LP RNFBs with good frequency characteristics are then derived. The LTI representation of the analysis filters and the use of cosine-roll-off characteristics allow us to design the analysis filters by the REMEZ exchange algorithm. Design examples of LP nearly perfect reconstruction (NPR) RNFBs are given to demonstrate the effectiveness of the proposed method.