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Nonuniqueness of the solution of the sound field reproduction problem

Fazi, Filippo and Nelson, P.A., (2010) Nonuniqueness of the solution of the sound field reproduction problem Noisternig, Markus and Misdariis, Nicolas (eds.) At 2nd International Symposium on Ambisonics and Spherical Acoustics, France. 06 - 07 May 2010. 6 pp.

Record type: Conference or Workshop Item (Paper)

Abstract

The sound field reproduction problem is formulated as an inverse problem, in which the reproduction of a target sound field is attempted, in the interior of a given control region, with an array of loudspeakers (referred to as a secondary source distribution). The determination of the loudspeaker gains represents an ill-posed problem. This paper studies under what circumstances the said inverse problem allows for a unique solution.The general solution of the problem is derived, and it is shown that nonuniqueness arises when the wave number is one of the Dirichlet eigenvalues of the control region. It is shown that, when this is not the case, the solution of the problem is unique. Numerical simulations illustrate the effect of nonuniqueness of the solution for the case of spherical secondary source distribution and control region. The case is also studied of the wave number being one of the Dirichlet eigenvalues of the region bounded by the secondary source distribution.

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More information

Published date: 17 June 2010
Venue - Dates: 2nd International Symposium on Ambisonics and Spherical Acoustics, France, 2010-05-06 - 2010-05-07

Identifiers

Local EPrints ID: 162031
URI: http://eprints.soton.ac.uk/id/eprint/162031
PURE UUID: 0a41bb99-f56e-4df3-a030-ccb14fd970b7

Catalogue record

Date deposited: 11 Aug 2010 16:11
Last modified: 18 Jul 2017 12:33

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Contributors

Author: Filippo Fazi
Author: P.A. Nelson
Editor: Markus Noisternig
Editor: Nicolas Misdariis

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