Nonuniqueness of the solution of the sound field reproduction problem
Nonuniqueness of the solution of the sound field reproduction problem
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.
Fazi, Filippo
e5aefc08-ab45-47c1-ad69-c3f12d07d807
Nelson, P.A.
5c6f5cc9-ea52-4fe2-9edf-05d696b0c1a9
Noisternig, Markus
f4628752-e82a-4373-b955-692ed3ca55cc
Misdariis, Nicolas
f636d0fa-ef9e-44cd-b993-91b7f58ba776
17 June 2010
Fazi, Filippo
e5aefc08-ab45-47c1-ad69-c3f12d07d807
Nelson, P.A.
5c6f5cc9-ea52-4fe2-9edf-05d696b0c1a9
Noisternig, Markus
f4628752-e82a-4373-b955-692ed3ca55cc
Misdariis, Nicolas
f636d0fa-ef9e-44cd-b993-91b7f58ba776
Fazi, Filippo and Nelson, P.A.
(2010)
Nonuniqueness of the solution of the sound field reproduction problem.
Noisternig, Markus and Misdariis, Nicolas
(eds.)
2nd International Symposium on Ambisonics and Spherical Acoustics, Paris, France.
05 - 06 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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Published date: 17 June 2010
Venue - Dates:
2nd International Symposium on Ambisonics and Spherical Acoustics, Paris, France, 2010-05-05 - 2010-05-06
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Local EPrints ID: 162031
URI: http://eprints.soton.ac.uk/id/eprint/162031
PURE UUID: 0a41bb99-f56e-4df3-a030-ccb14fd970b7
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Date deposited: 11 Aug 2010 16:11
Last modified: 02 Sep 2023 01:41
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Contributors
Editor:
Markus Noisternig
Editor:
Nicolas Misdariis
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