A review is presented of the fundamental principles underlying modern techniques for the active control of acoustic noise. The basic physical principles are first dealt with in the context of the active control of free field radiation and the classical approaches to the problem are briefly discussed. The active control of sound fields in ducts and enclosures is also described and the inherent physical limitations of the technique are emphasised. Modern signal processing methods for realising feedforward control systems are also outlined and least squares formulations are presented which enable performance limits to be established and adaptive algorithms to be derived.

Inverse filters can be designed in order to enhance the accuracy with which signals recorded in a given space can be reproduced in a given listening space. The problem is considered here of the design of an inverse filter matrix which enables K recorded signals to be accurately reproduced at K points in the listening space when transmitted via M loudspeaker channels. The analysis is sufficiently general to incorporate the case when the best (least squares) approximation is sought to the reproduction of K signals at L points in the space when LK. An analysis is presented which demonstrates that the approach suggested by the Multiple-Input/Output Inverse Filtering theorem of Miyoshi and Kaneda can be realised adaptively by using the Multiple Error LMS algorithm of Elliott et al.

We present a very fast method for calculating an inverse filter for audio reproduction system. The proposed method of FFT-based inverse filter design, which combines the well-known principles of least squares optimization and regularization, can be used for inverting systems comprising any number of inputs and outputs. The method was developed for the purpose of designing digital filters for multi-channel sound reproduction. It is typically several hundred times faster than a conventional steepest descent algorithm implemented in the time domain. A matrix of causal inverse FIR (finite impulse response) filters is calculated by optimizing the performance of the filters at a large number of discrete frequencies. Consequently, this deconvolution method is useful only when it is feasible in practice to use relatively long inverse filters. The circular convolution effect in the time domain is controlled by zeroth-order regularization of the inversion problem. It is necessary to set the regularization parameter β to an appropriate value, but the exact value of β is usually not critical. For single-channel systems, a reliable numerical method for determining β without the need for subjective assessment is given. The deconvolution method is based on the analysis of a matrix of exact least squares inverse filters. The positions of the poles of those filters are shown to be particularly important.