Plane-wave decomposition analysis for spherical microphone arrays

TitlePlane-wave decomposition analysis for spherical microphone arrays
Publication TypeConference Papers
Year of Publication2005
AuthorsDuraiswami R, Li Z, Zotkin DN, Grassi E, Gumerov NA
Conference NameIEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2005
Date Published2005/10//
ISBN Number0-7803-9154-3
KeywordsAcoustic propagation, Acoustic scattering, acoustic signal processing, acoustic waves, array signal processing, band-limit criteria, beamforming, Educational institutions, Fourier transforms, Frequency, Laboratories, microphone arrays, Nails, Nyquist criterion, Nyquist-like criterion, Partial differential equations, plane-wave decomposition analysis, sound field analysis, spherical microphone arrays, spherical wave-functions

Spherical microphone arrays have attracted attention for analyzing the sound field in a region and beamforming. The analysis of the recorded sound has been performed in terms of spherical wave-functions, and recently the use of plane-wave expansions has been suggested. We show that the plane-wave basis is intimately related to the spherical wave-functions. Reproduction in terms of both representations satisfies certain band-limit criteria. We provide an error bound that shows that to reproduce the spatial characteristics of a sound of a certain frequency we need to be able to accurately represent sounds of up to a particular order, which establishes a Nyquist-like criterion. The order of the sound field in turn is related to the number of microphones in the array necessary to achieve accurate quadrature on the sphere. These results are illustrated with simulations.