Unifying spherical harmonic and 2-D Fourier decompositions of the array manifold

Authors:
Mário Costa;Visa Koivunen;Andreas Richter
Affiliations:
Helsinki University of Technology, Department of Signal Processing and Acoustics, SMARAD CoE, TKK, Finland;Helsinki University of Technology, Department of Signal Processing and Acoustics, SMARAD CoE, TKK, Finland;Nokia Research Center, Nokia Group, Finland
Venue:
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Year:
2009

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Abstract

In this paper, a unified framework for orthonormal decomposition of the array manifold is derived. An equivalence between spherical harmonics and 2-D Fourier basis functions is established. Consequently, a link between spherical harmonic spectra and 2- D Fourier spectra is found. Moreover, the spherical harmonic and 2-D Fourier decompositions of the array manifold vector, i.e. Wavefield Modeling and 2-D Effective Aperture Distribution Function (EADF) are shown to be equivalent. The rotation of functions on the 2-D Fourier domain is discussed.