A new method for designing linear-phase recombination nonuniform filter-banks

This paper proposes a design method of linear-phase (LP) recombination nonuniform filter-banks (RNFBs), where certain channels of a uniform filter-bank (FB) are merged by sets of transmultiplexors (TMUXs). The case where the numbers of channels of the uniform FB and the TMUXs are not coprime to each other is studied in detail. By analyzing the spectrum supports of the analysis filters, it is found that the uniform FB and recombination TMUXs in the LP RNFBs can be designed separately as long as certain conditions are satisfied. This significantly simplifies the design procedure. Using this result, the design of a class of nearly PR LP RNFBs with cosine roll-off transition band based on the REMEZ algorithm is studied. Design examples show that LP RNFBs with good frequency responses and reasonably low reconstruction error can be obtained readily by the proposed method.