Spherical Harmonic Analysis of Wavefields Using Multiple Circular Sensor Arrays

Spherical harmonic decomposition of wavefields is not only an active problem in acoustic signal processing but also a useful tool in a plethora of applications such as 3-D beamforming, direction of arrival estimation, and spatial sound recording. This paper presents a novel array structure consisting of a set of parallel circular arrays of sensors to decompose a wavefield into spherical harmonic components. The new structure presented here provides an alternative design to the traditional spherical microphone arrays with increased flexibility on sensor locations. We use the underlying structure of the wave propagation together with the properties of the associated Legendre functions and the spherical Bessel functions to develop a systematic approach to place circular arrays and construct a hybrid array. As an illustration, we design a fifth-order spherical harmonic decomposition array using 57 microphones to operate over a frequency band of an octave and compare it with a spherical array. We use computer simulations to show the performance of the array in a beamforming example.