Applications of adaptive filters in active noise control

Abstract

The active reduction of acoustic noise is achieved by the addition of a cancelling acoustic signal to the unwanted sound. Successful definition of the cancelling signal amounts to a system identification problem. Recent advances in adaptive signal processing have allowed this problem to be tackled using adaptive filters, which offer significant advantages over conventional solutions. This thesis is devoted to the study of the extension of adaptive noise cancelling techniques, which were developed in the electrical signal conditioning context, to the control of acoustic systems. An analysis is presented of the behaviour of the Widrow-Hoff LMS adaptive noise canceller with a linear filter in its control loop. 'Equivalent Transfer Function' descriptors of the system are derived which are linear, time invariant for certain classes of input signal, typical of acoustical applications. This allows the influence of the control loop filter upon the adaptive filter to be analysed using conventional techniques, including the exact specification of the stability limits imposed by the control loop filter. The active control of plane waves propagating axially in a hardwalled duct is used as a motivating model problem. All of the electrical, electroacoustic and acoustic transfer functions in this application may be modelled by a single equivalent control loop filter, allowing the behaviour of the adaptively controlled system to be investigated using the equivalent transfer function approach. The equivalent transfer functions are extended to cover techniques for compensating the adaptive filter for the damaging consequences of the control loop filter. This allows an analytical approach to the design of compensating filters and suggests some formal compensator design rules. The model problem also motivates the study of the effects of feedback around an LMS adaptive filter. Such feedback is shown to be typical of many acoustical applications of the adaptive cancelling technique. The time variance and non-linearity introduced into the system equations, which preclude generalised analysis, are illustrated. An alternative stochastic gradient algorithm for controlling adaptive filters in the presence of feedback is presented. The theoretical work presented in this thesis is supported by experimental results, demonstrating the design and performance of compensated adaptive acoustic noise controllers.

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