Subband decomposition: an LMS-based algorithm to approximate the perfect reconstruction bank in the general case

An algorithm based on least mean squares (LMS) is described. Given an arbitrary invertible decomposition/decimation process, the algorithm will find the finite impulse response reconstruction filters which best approximate the perfect reconstruction ones. By allowing the reconstruction filters' impulse responses to be sufficiently long, the quality of the approximation can be made as good as required. Two examples are presented for the implementation of this algorithm: one in the case of a decomposition by a filter bank of Galand (1977), where the reconstruction bank is already known, the other in the situation of a two-subband decomposition where one of the subbands covers two-thirds of the frequency space, and the other covers the remaining one-third.<
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