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