Equivalence between multirate filter bank and circular lattice filter and its application in statistically matched multirate filter bank

Abstract

In this paper we address the issue of finding multirate filter bank matched to a given signal. The salient contributions, of this paper can be summarized as follows: (i) a precise mathematical equivalence, between M-channel circular lattice filter and M-band multirate filter bank, is established; (ii) the concept of signal matched analysis filter bank is defined. Also a precise mathematical formulation is presented which makes it possible to regard the signal matched analysis filter bank as single input multiple output prediction error system or as a whitening filter bank; (iii) it is observed that the problem of finding signal matched analysis bank is mathematically same as vector AR modeling and whitening problem; (iv) with the observation (iii) and the equivalence result of (i) at our disposal, we address the problem of finding signal matched analysis side multirate filter bank. (v) The concept of signal matched synthesis bank is defined. Also a precise mathematical formulation is presented for finding the parameters of the filter bank. We also present simulation results to validate the theory.