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.>

We measured the responses of a circumaural and a supraaural headphone on 14 subjects and a head and torso simulator (HATS) with a simplified ear simulator terminated in a resistance, which has been originally developed for the simulated in-situ measurements of hearing aids. The sound pressure at the earcanal entrance of the subjects and the HATS was picked up by the probe tube microphone. The headphones were excited by white noise and their frequency responses were calculated by cross spectrum method for FIR system identification. The measured headphone responses on the HATS agree with the average responses of the real ears below 6 kHz.