Boaz Rafaely

Analysis and design of spherical microphone arrays

Spherical microphone arrays have been recently studied for sound-field recordings, beamforming, and sound-field analysis which use spherical harmonics in the design. Although the microphone arrays and the associated algorithms were presented, no comprehensive theoretical analysis of performance was provided. This work presents a spherical-harmonics-based design and analysis framework for spherical microphone arrays. In particular, alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations. The analysis framework can also provide a useful guide for the design and analysis of more general spherical microphone arrays which do not use spherical harmonics explicitly.

Microphone array signal processing

This article reviews Microphone Array Signal Processing by Jacob Benesty, Jingdong Chen, Yiteng Huang , Berlin, 2008. 240 pp. price

Plane-wave decomposition of the sound field on a sphere by spherical convolution

119 (hardcover). ISBN: 3540786112

Spatial Aliasing in Spherical Microphone Arrays

Spherical microphone arrays have been recently studied for sound analysis and sound recordings, which have the advantage of spherical symmetry facilitating three-dimensional analysis. This paper complements the recent microphone array design studies by presenting a theoretical analysis of plane-wave decomposition given the sound pressure on a sphere. The analysis uses the spherical Fourier transform and the spherical convolution, where it is shown that the amplitudes of the incident plane waves can be calculated as a spherical convolution between the pressure on the sphere and another function which depends on frequency and the sphere radius. The spatial resolution of plane-wave decomposition given limited bandwidth in the spherical Fourier domain is formulated, and ways to improve the computation efficiency of plane-wave decomposition are introduced. The paper concludes with a simulation example of plane-wave decomposition.

Sound-field analysis by plane-wave decomposition using spherical microphone array

Performance of microphone arrays at the high-frequency range is typically limited by aliasing, which is a result of the spatial sampling process. This paper presents analysis of aliasing for spherical microphone arrays, which have been recently studied for a range of applications. The paper presents theoretical analysis of spatial aliasing for various sphere sampling configurations, showing how high-order spherical harmonic coefficients are aliased into the lower orders. Spatial antialiasing filters on the sphere are then introduced, and the performance of spatially constrained filters is compared to that of the ideal antialiasing filter. A simulation example shows how the effect of aliasing on the beam pattern can be reduced by the use of the antialiasing filters

Phase-mode versus delay-and-sum spherical microphone array processing

Directional sound-field information is becoming more important in sound-field analysis and auditorium acoustics, and, as a consequence, a variety of microphone arrays have recently been studied that provide such information. In particular, spherical microphone arrays have been proposed that provide three-dimensional information by decomposing the sound field into spherical harmonics. The theoretical formulation of the plane-wave decomposition and array performance analysis were also presented. In this paper, as a direct continuation of the recent work, a spherical microphone array configured around a rigid sphere is designed, analyzed using simulation, and then used experimentally to decompose the sound field in an anechoic chamber and an auditorium into waves. The array employs a maximum of 98 measurement positions around the sphere, and is used to compute spherical harmonics up to order 6. In the current paper we investigate the factors affecting the performance of plane-wave decomposition, showing that...

Open-Sphere Designs for Spherical Microphone Arrays

Phase-mode spherical microphone array processing, also known as spherical harmonic array processing, has been recently studied for various applications. The spherical array configuration provides desired three-dimensional symmetry, while the phase modes provide frequency-independent spatial processing. This letter employs the spherical harmonic framework to compare the well-known delay-and-sum to the phase-mode processing for spherical arrays. The two approaches show similar performance at frequencies where the upper spherical harmonic order equals the product of the wave number and sphere radius. However, at lower frequencies, phase-mode processing maintains the same directivity, limited by signal-to-noise ratio, while for delay-and-sum, spatial resolution deteriorates.

The Spherical-Shell Microphone Array

Spherical microphone arrays have been studied for a wide range of applications, one of which is acoustic measurement and analysis. Since a minimal interaction between the array and the measured sound field is an advantage in this case, open-sphere arrays are preferable compared to rigid-sphere arrays. However, it has been shown that open-sphere arrays suffer from numerical ill-conditioning at frequencies which correspond to the nodal values of the spatial spherical modes with the result of excessive noise at these frequencies. A method for overcoming this problem using an open dual-sphere array is proposed in this correspondence and then investigated and compared to an array configured around a rigid sphere and an array composed of cardioid microphones. An optimal value for the ratio of the two spheres is derived, and simulation examples illustrating the advantage of the dual-sphere array are finally presented

Spatial-temporal correlation of a diffuse sound field

Spherical microphone arrays have been recently studied for a wide range of applications. In particular, microphones arranged around an open or virtual sphere are useful in scanning microphone arrays for sound field analysis. However, open-sphere spherical arrays have been shown to have poor robustness at frequencies related to the zeros of the spherical Bessel functions. This paper presents a framework for the analysis of array robustness using the condition number of a given matrix, and then proposes several robust array configurations. In particular, a dual-sphere configuration previously presented which uses twice as many microphones compared to a single-sphere configuration is analyzed. This paper then shows that high robustness can be achieved without increasing the number of microphones by arranging the microphones in the volume of a spherical shell. Another simpler configuration employs a single sphere and an additional microphone at the sphere center, showing improved robustness at the low-frequency range. Finally, the white-noise gain of the arrays is investigated verifying that improved white-noise gain is associated with lower matrix condition number.

Spherical Microphone Array Beamforming

The spatial correlation function of the sound in a diffuse field is a quantity widely used in many reverbrant room acoustic applications. Although results for the spatial and temporal correlation for pure-tone and band-limited diffuse fields have already been developed, these have not been generalized for other signal types. This work presents a generalized derivation of the diffuse field spatial-temporal correlation which can be used for stationary random signals with given power spectral density. It is shown that the spatial-temporal correlation depends entirely on the temporal correlation of the signal exiting the diffuse field, or alternatively on its power spectral density. A simulation using the plane wave model is presented for tonal and broadband diffuse sound fields.