Theoretical Advances in Multichannel Crosstalk Cancellation Systems

Abstract

This thesis is concerned with the development of physical models of multichannel crosstalk cancellation (CTC) systems and the analysis of those models. The physical principles of multichannel CTC systems are established through a course of analytical studies that rely on the singular value decomposition (SVD), eigendecomposition, and a novel analysis framework that was developed in the course of these investigations. In the first of these studies, a simple acoustic model is introduced and the singular system for asymmetric and symmetric geometries is derived. An analysis of the low frequency source strength solution leads to an amplitude panning function that is shown to be a solution to the multichannel sine law. The eigenvalues of the Gram matrix reveal that the system is generally dependent on a phenomenon identified as focusing crosstalk. In the second of these works, it is shown that the multichannel CTC system robustness and stability, as quantified by the system condition number and amplification factor of the pseudoinverse, respectively, can be described directly in terms of the focusing crosstalk at a single point. This realisation leads to a physical study of the symmetric CTC system and the focusing behaviour of specific multichannel geometries. In the absence of reflections, the focusing crosstalk is largely due to sidelobe radiation, and thus an intuitive link is formed between the physical concepts of beamforming and the stability of the inverse solution. In the third of these works, the analysis culminates in an examination of the general underdetermined linear discrete inverse problem in the context of sound-field control, and is centred on the focusing behaviour inherent to the inverse solution. The physical requirements for optimally-conditioned systems are rigorously established and shown to occur only when the focusing crosstalk is minimised at all control points in the field. Finally, an alternate method to achieve CTC is developed based on the derived source strength modes of an optimally-conditioned system. The practical implications of these physical studies are discussed and supported with simulations using measured data.

More information

Identifiers

ORCID for Filippo Fazi: orcid.org/0000-0003-4129-1433

Catalogue record

Export record