Spherical sector harmonics representation of sound fields using a microphone array over spherical sector.

Abstract

Spherical microphone arrays (SMAs) are widely used for sound recording and analysis, with processing being done in the spherical harmonics (SH) domain. This is due to the ease of array processing in the SH domain without spatial ambiguity. However, it is uneconomical to construct a full SMA when sources are present in restricted regions of the environment. Additionally, the use of a full SMA comes at the cost of more microphone signals to process. Attempts have been made to use hemispherical microphone arrays on the basis of the acoustic image principle, enabling application of SH but with greater computational complexity. In this paper, the use of a spherical sector microphone array instead of a full SMA is proposed. An orthonormal spherical sector harmonics (S2H) basis function is developed for accurate representation of pressure over the sector. The orthonormality of the S2H function is established using orthogonality of shifted associated Legendre polynomials and a scaled exponential function. An addition theorem for S2H basis functions is derived. The S2H basis function is applied to the decomposition of a sound field over a sector array. The S2H basis function has potential applications to brain source localization and physiological shape description.