Abstract
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.
Highlights
Crosstalk cancellation (CTC) systems are designed to deliver a binaural signal at the ears of a listener using loudspeakers rather than headphones [1,2]
The results show that the derived low frequency source strengths are a one-to-one match to the numerical solution of
The singular value decomposition of the L-channel single-listener CTC system was derived for asymmetric and symmetric geometries assuming far-field monopole sources in free-field and a shadowless head
Summary
Crosstalk cancellation (CTC) systems are designed to deliver a binaural signal at the ears of a listener using loudspeakers rather than headphones [1,2]. It is useful to understand what physical parameters influence the condition number and energy requirement of multichannel CTC systems To aid in such an analysis researchers in sound-field control have employed the singular value decomposition (SVD) as a tool to analyse the radiation matrix and its inverse. When geometric symmetry is enforced about the median plane the low frequency source strengths are the minimum 2 norm solution of the multichannel sine law This result bridges two well-established sound reproduction techniques, amplitude panning and CTC, under the same inverse problem framework.
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