The condition number of the matrix of electro-acoustic head-related transfer functions (HRTF) in a two-channel sound reproduction system has been used as a measure of robustness of the Atal-Schroeder (1962) crosstalk canceler. A comparative study has been made using results produced by computer simulations and HRTFs measured in an anechoic chamber by means of a dummy head. It has been found that acoustic scattering by the head has a very important and beneficial influence on robustness, specially for large loudspeaker separations. For narrow loudspeaker separations of less than about 40 degrees it is found that crosstalk cancellation exhibits a large variation of alternating very low and very high robustness. Also, simulations and measurements have been made of the natural channel separation under the same conditions. Scattering by the head is seen to provide a good level of natural channel separation at high frequencies and large loudspeaker angles. At low frequencies or small loudspeaker angles natural channel separation is poor.

A very fast deconvolution method, which is based on the fast Fourier transform (FFT), can be used to control the outputs from a multichannel plant comprising any number of control sources and error sensors. The result is a matrix of causal finite impulse response filters whose performance is optimized at a large number of discrete frequencies. The paper is particularly aimed at multichannel sound reproduction and more specifically reproducing the sound field from a set of loudspeakers.

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.>