Errors in two-point sound reproduction

This paper deals with the problem of reproducing two signals at two points in space by using two acoustic sources. While much is now known about the techniques available for the design of matrices of inverse filters that enable this objective to be achieved in practice, it is still the basic physics of the sound field produced that controls the effectiveness of such systems and which ultimately dictates their design. The basic physical processes involved in producing the cross-talk cancellation that enables the reproduction of the desired signals is revisited here by using a simple two source/two field point free field model. The singular value decomposition is used to identify those frequencies where the inversion problem becomes ill-conditioned and to explain physically the origin of the ill-conditioning. As observed previously, it is found that cross-talk cancellation becomes problematic when the path length difference between the two sources and one of the field points becomes equal to one half the acoustic wavelength. The ill-conditioned frequencies are also found to be associated with a limited spatial region of cross-talk cancellation and with large source outputs manifested in the time domain by responses of long duration.