Matrix Adaptive Synthesis Filter for Uniform Filter Bank

TL;DR

This paper introduces a matrix adaptive filter approach for the synthesis stage of a uniform filter bank, utilizing Wiener filtering theory and LMS adaptation to improve signal reconstruction.

Contribution

It develops a mathematical framework for adaptive synthesis filtering in uniform filter banks using Wiener filter theory and demonstrates convergence with LMS adaptation.

Findings

Adaptive filter converges to a stable Wiener solution

LMS algorithm effectively updates synthesis filter coefficients

Improved signal reconstruction in uniform filter banks

Abstract

In this paper, we use a matrix adaptive filter as the synthesis stage of a Uniform Filter Bank (UFB) to reconstruct the input signal. We first develop the mathematical theory behind it by applying the model of optimal filtering at the synthesis stage of the UFB and obtaining an expression for the matrix Wiener filter. We have developed a theorem which we use to simplify the expression further. In the absence of required information about the analysis stage, we use adaptive filtering to arrive at the Wiener solution. We use the Least Mean Square (LMS) algorithm to update the filter coefficients. Through experimental results, we find that the adaptive filter is convergent for a stable Wiener filter.