Exact Least Squares Algorithm for Signal Matched Multirate Whitening Filter Bank: Part I

TL;DR

This paper introduces an exact least squares algorithm for a signal matched multirate whitening filter bank that optimally whitens signals across channels, with recursive algorithms for filter coefficient estimation, validated through simulations.

Contribution

It presents a novel recursive least squares algorithm for designing a signal matched multirate whitening filter bank with a lattice structure, including coefficient estimation methods.

Findings

Algorithm effectively whitens Gaussian and non-Gaussian processes.

Recursive approach offers computational efficiency.

Simulation results confirm theoretical validity.

Abstract

In this paper, we define a concept of signal matched multirate whitening filter bank which provides an optimum coding gain. This is achieved by whitening the outputs, of the analysis filter bank, within as well as across the channels, by solving a constrained projection problem. We also present a fast time and order recursive least squares algorithm to obtain the vector output of the proposed analysis filter bank. The recursive algorithm, developed here, gives rise to a lattice-like structure. Since the proposed signal matched analysis filter bank coefficients are not available directly, an order recursive algorithm is also presented for estimating these from the lattice parameters. Simulation results are presented to validate the theory. It is also observed that the proposed algorithm can be used to whiten Gaussian/non-Gaussian processes with minimum as well as non-minimum phase.