Design of perfect-reconstruction nonuniform recombination filter banks with flexible rational sampling factors

This paper studies the design of a class of perfect-reconstruction (PR) nonuniform filter banks (FBs) called recombination nonuniform FBs (RNFBs). They are constructed by merging subbands in a uniform FB with sets of transmultiplexers (TMUXs). It generalizes the RNFBs previously proposed by the authors to allow more general choice of the sampling factors. The spectral inversion and spurious response suppression problems of these new RNFBs using cosine modulation are analyzed, and a simple design method based on a matching condition is proposed. It is also found that the FB and the TMUX in the recombination structure can be designed separately to satisfy the matching condition. In addition, real-time adaptive merging of the channels to provide dynamic nonuniform frequency partitioning is feasible. Another advantage of the RNFBs is that the recombination and processing of the subband signal can be done at the decimated domain of the uniform FB, which greatly reduces its implementation complexity. Design examples show that high quality nonuniform PR FBs with low implementation complexity and variable time-frequency resolution can be obtained by the proposed method.