Plane-wave decomposition of the sound field on a sphere by spherical convolution

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Abstract

Spherical microphone arrays have been recently studied for sound analysis and sound recordings, which have the advantage of spherical symmetry facilitating three-dimensional analysis. This paper complements the recent microphone array design studies by presenting a theoretical analysis of plane-wave decomposition given the sound pressure on a sphere. The analysis uses the spherical Fourier transform and the spherical convolution, where it is shown that the amplitudes of the incident plane waves can be calculated as a spherical convolution between the pressure on the sphere and another function which depends on frequency and the sphere radius. The spatial resolution of plane-wave decomposition given limited bandwidth in the spherical Fourier domain is formulated, and ways to improve the computation efficiency of plane-wave decomposition are introduced. The paper concludes with a simulation example of plane-wave decomposition.

Original languageEnglish
Pages (from-to)2149-2157
Number of pages9
JournalJournal of the Acoustical Society of America
Volume116
Issue number4 I
DOIs
StatePublished - 1 Oct 2004

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