A modal analysis of multichannel crosstalk cancellation systems and their relationship to amplitude panning

The single-listener multichannel crosstalk cancellation system is analysed using the singular value decomposition. Analytic expressions for the singular system are derived considering a sound-field of point sources placed in the far-field and in free-field conditions. The derived singular system yields theoretical insight into the benefit of multichannel loudspeaker geometries over the conventional two-channel system. From the singular system the source strength solution is derived for a target far-field virtual source. The low frequency approximation of the derived source strengths is an amplitude panning function. This panning function is a generalisation of the sine law solution that allows for head rotation and asymmetric loudspeaker geometry. When the geometry is symmetric about the median plane of the listener the low frequency sources strengths are the minimum ℓ2 norm solution of the multichannel sine law. The low frequency approximation is also shown to be representative when the free-field assumption is relaxed.