Spherical Harmonic Analysis of Wavefields Using Multiple Circular Sensor Arrays

Abstract

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 3D 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.

Parameterization of the three-dimensional room transfer function in horizontal plane

“…Therefore, we adopt the conversion relationship between azimuth harmonic coefficients and spherical harmonic coefficients 15 to derive horizontal plane RTF coefficients. Based on the azimuth harmonic decomposition, we can calculate the azimuth harmonic coefficients c ðq 0 ;n 0 ;m 0 Þ l ðkÞ of the reverberant path on the q 0 th circle (q 0 ¼ 1, 2,…, Q 0 ) using the following approximation:…”

Three-Dimensional Sound Field Reproduction Using Multiple Circular Loudspeaker Arrays

“…Step 3 (m = N − 2 series): In this case, we need to calculate three aperture function coefficients to control three harmonic sound field coefficients α (24) 4 A complete guideline to choosing elevation angles for even and odd associated Legendre functions are given in [32]. …”

Acoustic Sources Localization in 3D Using Multiple Spherical Arrays

“…To get better performance, spherical harmonic analysis considering the physical characteristics of wave propagation in the air is applied to MUSIC and ESPRIT algorithms based on spherical microphone arrays [16]. The sound field is decomposed into spherical harmonic components by sampling the field using spherical harmonic analysis technique [17,18]. One of the main advantages of performing the analysis in the spherical harmonic component domain is the fact that the frequency-dependent components are decoupled from the angular-dependent components which provides a new perspective on related array processing problems such as source localization and detection.…”

“…Notice that when using the spherical harmonic analysis techniques, the microphones of the traditional array are arranged regularly, such as circular array or spherical array [18,[22][23][24]. More importantly, only single array is used in all the former related study [25][26][27][28].…”