Non Spherical Microphone Array Structures for 3d Beamforming and Spherical Harmonic Analysis

Decomposition of a soundfield into spherical harmonics is a fundamental problem in acoustic signal processing. This paper shows how to design non-spherical microphone array structures in 3D space to decompose a soundfield into spherical harmonic components. We use the mode limiting property of the Bessel functions and zeros of the associated Legendre functions together with orthoganality of the exponential functions over circles to construct an array of parallel circles of microphones. The result provides flexible design guidelines to construct 3D arrays than traditional spherical arrays. A simple beamforming example is given to verify the result.