A multi-channel audio system based on the theory of integral equations

• Published in: The Journal of the Acoustical Society of America Vol. 125; no. 4_Supplement; p. 2543
• Main Authors: Fazi, Filippo M., Nelson, Philip A.
• Format: Journal Article
• Language: English
• Published: 01-04-2009
• ISSN: 0001-4966; 1520-8524
• DOI: 10.1121/1.4783610

The basics of a multi-channel audio system, which attempts the reproduction of a desired sound field, are presented. The system’s hardware consists of a three-dimensional array of loudspeakers, and can be used in combination with a specially designed microphone array. The mathematical fundamentals on which this technique is grounded consist of the formulation of the problems as an integral equation. The loudspeaker signals are determined from the knowledge of the target sound field on the boundary of a given control volume. The solution to this inverse problem is computed performing a singular value decomposition of the integral operator involved. For some simple array geometries it is possible to calculate an analytical solution to the problem. A regularization method is applied, as required by the ill-posed nature of the inverse problem under consideration. Some insight into the physical meaning of the ill-posedness is given and some analogies to near-field acoustic holography are suggested. The effectiveness of the method proposed has been verified experimentally and some of the experimental results are presented. Finally, it is shown how this technique has been successfully applied to the design of a multi-channel auralization system for room acoustics.