Inverse filter design and equalization zones in multichannel sound reproduction

A discussion is given of two techniques for designing inverse filters for use in multichannel sound reproduction systems. The first is the multiple-input/output inverse filtering theorem, which uses direct inversion of a matrix containing the coefficients of filters used to specify the electroacoustic transmission paths. The second is an adaptive technique based on the multiple error LMS algorithm. The theory presented reconciles the two approaches and furthermore, derives explicit conditions which must be fulfilled if an exact inverse is to exist. A formula is derived which gives the number of coefficients required in the inverse filters in terms of the number of coefficients used to represent the transmission paths. Some numerical examples are also presented which illustrate the dependence of the mean square error on both the choice of modeling delay and the number of coefficients in the inverse filters. Finally, the results of some simulations are given which demonstrate the acoustical possibilities associated with these filtering techniques