Transfer functions of FXLMS-based Multi-channel Multi-tone Active Noise Equalizers

TL;DR

This paper presents a method to calculate and analyze transfer functions of FXLMS-based multi-channel multi-tone active noise equalizers, aiding in verification and prediction of their behavior across the spectrum.

Contribution

It introduces a way to compute transfer functions for these equalizers, enabling better understanding and prediction of their spectral behavior and convergence properties.

Findings

Transfer functions can be accurately calculated at noise frequencies.

Analysis helps verify equalizer settings and predict convergence.

Provides practical insights beyond statistical convergence analysis.

Abstract

Multi-channel Multi-tone Active Noise Equalizers can achieve different user-selected noise spectrum profiles even at different space positions. They can apply a different equalization factor at each noise frequency component and each control point. Theoretically, the value of the transfer function at the frequencies where the noise signal has energy is determined by the equalizer configuration. In this work, we show how to calculate these transfer functions with a double aim: to verify that at the frequencies of interest the values imposed by the equalizer settings are obtained, and to characterize the behavior of these transfer functions in the rest of the spectrum, as well as to get clues to predict the convergence behaviour of the algorithm. The information provided thanks to these transfer functions serves as a practical alternative to the cumbersome statistical analysis of convergence, whose results are often of no practical use.