An active noise control algorithm with gain and power constraints on the adaptive filter

Walter J Kozacky,Tokunbo Ogunfunmi

doi:10.1186/1687-6180-2013-17

Walter J Kozacky, Tokunbo Ogunfunmi

Open Access

https://doi.org/10.1186/1687-6180-2013-17

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Abstract

This article develops a new adaptive filter algorithm intended for use in active noise control systems where it is required to place gain or power constraints on the filter output to prevent overdriving the transducer, or to maintain a specified system power budget. When the frequency-domain version of the least-mean-square algorithm is used for the adaptive filter, this limiting can be done directly in the frequency domain, allowing the adaptive filter response to be reduced in frequency regions of constraint violation, with minimal effect at other frequencies. We present the development of a new adaptive filter algorithm that uses a penalty function formulation to place multiple constraints on the filter directly in the frequency domain. The new algorithm performs better than existing ones in terms of improved convergence rate and frequency-selective limiting.

Highlights

Active noise control (ANC) systems can be used to remove interference by generating an anti-noise output that can be used in the system to destructively cancel the interference [1]
In a frequency-domain implementation of the least-mean-square (LMS) algorithm, the limiting constraints can be placed directly in the frequency domain, allowing the adaptive filter response to be reduced in the frequency regions of constraint violation, with minimal effect at other frequencies [2]
We develop a new class of gain-constrained and power-constrained algorithms termed constrained minimal disturbance (CMD)

Summary

Introduction

Active noise control (ANC) systems can be used to remove interference by generating an anti-noise output that can be used in the system to destructively cancel the interference [1]. Gain-constrained algorithm At each block update m, the new algorithm will minimize the squared Euclidean norm of the frequencydomain weight change in each individual frequency bin k, where the weight change is given by δWkðm þ 1Þ 1⁄4 Wkðm þ 1Þ À WkðmÞ; ð11Þ subject to the condition of a posteriori filter convergence in the frequency domain. Following a development similar to the gain-constrained case results in the CMD algorithm given by (31) using a new diagonal matrix of leakage factors (32). Following a development similar to the gain-constrained case, and using a new diagonal matrix of leakage factors (32) results in the CMD algorithm, repeated below. 4. Convergence analysis We assume that all signals are white, zero-mean, Gaussian wide-sense stationary, and employ the independence assumption [7] under a steady-state condition, where the constraint violation is constant and the transform-domain weights are mutually uncorrelated (which occurs as the filter size N grows large [16]). When these conditions are satisfied the result is lim m→1

Mean value

10 CSD Algorithm CMD Algorithm

Findings

Conclusion