Rigid Spherical Microphone Array Research Articles

Time-domain sound field reconstruction using a rigid spherical microphone array.

A time-domain approach for interior spherical near-field acoustic holography is proposed to achieve the low-delay reconstruction of time-domain sound fields using a rigid spherical microphone array. This reconstruction encompasses the incident pressure field, the incident radial particle velocity field, and the total pressure field, which includes scattering. The proposed approach derives time-domain radial propagators through the inverse Fourier transform of their frequency-domain counterparts. These propagators are then applied to the array measurements to obtain the time-domain spherical harmonic coefficients of the interior sound field. Given the fact that the time-domain radial propagators possess finite-time support and exhibit significant high-frequency attenuation characteristics, they can be efficiently implemented using finite impulse response (FIR) filters. The proposed approach processes the signal sample-by-sample through these FIR filters, avoiding a series of issues associated with time-frequency transformations in frequency-domain methods. As a result, the approach offers higher accuracy and lower latency in reconstructing non-stationary sound fields compared to its frequency-domain counterpart and thus holds greater potential for real-time applications. Additionally, owing to the scattering effect of the rigid sphere, the approach avoids the impact of spherical Bessel function nulls and does not require the measurement of particle velocities, which renders the measurements cost effective.

Multiple scattering ambisonics: Three-dimensional sound field estimation using interacting spheres.

Rigid spherical microphone arrays (RSMAs) have been widely used in ambisonics [Gerzon (1973). J. Audio Eng. Soc. 21, 2-10] sound field recording. While it is desired to combine the information captured by a grid of densely arranged RSMAs for expanding the area of accurate reconstruction, or sweet-spots, this is not trivial due to inter-array interference. Here, we propose multiple scattering ambisonics, a method for three-dimensional ambisonics sound field recording using multiple acoustically interacting RSMAs. Numerical experiments demonstrate the sweet-spot expansion realized by the proposed method. The proposed method can be used with existing RSMAs as building blocks and opens possibilities including higher degrees-of-freedom spatial audio.

Sparse Representations With Legendre Kernels for DOA Estimation and Acoustic Source Separation

Recording multiple sound sources in a reverberant environment results in convolutive mixtures. Sound sources can be extracted from microphone array recordings of such mixtures using acoustic source separation techniques. Acoustic source separation using recordings obtained from rigid spherical microphone arrays (RSMA) benefit from the representation of sound fields as series of spherical harmonics. More specifically, RSMAs afford increased flexibility in acoustic beamforming and spatial filtering. We propose a data-driven DOA estimation and acoustic source separation method based on a dictionary-based sparse decomposition of sound fields. The proposed method involves identifying the time-frequency bins with contributions from a single source only and those with sensor noise or diffuse sound field components. The former set of bins is used in DOA estimation and beamforming in the sparse decomposition domain. The latter set is used to calculate the diffuse field covariance matrix used in Wiener post-filtering to improve the source separation performance further. We demonstrate the utility of the proposed method via extensive objective and subjective evaluations.

Three-dimensional source localization using sparse Bayesian learning on a spherical microphone array.

The identification of acoustic sources in a three-dimensional (3D) domain based on measurements with an array of microphones is a challenging problem: it entails the estimation of the angular position of the sources (direction of arrival), distance relative to the array (range), and the quantification of the source amplitudes. A 3D source localization model using a rigid spherical microphone array with spherical wave propagation is proposed. In this study, sparse Bayesian learning is used to perform localization in 3D space and examine the use of principal component analysis to denoise the measurement data. The performance of the proposed method is examined numerically and experimentally, which is tested both in a free-field and in a reverberant environment. The numerical and experimental investigations demonstrate that the approach offers accurate localization in a 3D domain, resolving closely spaced sources and making it possible to identify sources located at different ranges.

Compressive Spherical Beamforming for Acoustic Source Identification

This study examines a compressive spherical beamforming (CSB) method, using a rigid spherical microphone array to localize and quantify the acoustic contribution of sources. The method relies on the array signal model in the spherical harmonics domain that can be represented as a spatially sparse problem. This makes it possible to use compressive sensing to solve an underdetermined problem via promoting sparsity. The estimation of the angular position of sources with respect to the microphone array, as well as the three-dimensional localization over a volume are investigated. Several sparse recovery algorithms [orthogonal matching pursuit (OMP), generalized OMP, ϱ1-norm minimization, and reweighted ϱ1-norm minimization] are examined for this purpose. The numerical and experimental results indicate that sparse recovery methods outperform conventional spherical harmonics beamforming. Reweighted ϱ1-norm has good adaptability to noise, improving the robustness of CSB. The method can successfully localize the angular position of sources, and quantify their relative pressure contribution. The method is promising to localize sources in a three-dimensional domain of interest. However, the three-dimensional localization is more sensitive to noise, source distance, and properties of the sensing matrix than the two-dimensional localization.

Iteratively Reweighted Spherical Equivalent Source Method for Acoustic Source Identification

Spherical equivalent source method (S-ESM) using rigid spherical microphone arrays can simultaneously identify sound sources in all directions. In this paper, based on the reweighting and sparse representation frameworks, the sparsity-promoting iteratively reweighted least squares (IRLS) and reweighted l 1 -norm minimization (referred as w-l 1 -norm) are exploited to improve the performance of acoustic source identification for S-ESM. The numerical and experimental results indicate accurate acoustic source identification for the two iteratively reweighted algorithms. IRLS can provide good acoustic source identification over the wide frequency and measurement distance ranges, improving the performance of the established S-ESM. In addition, w-l 1 -norm is also an alternative solution strategy for S-ESM, although at the expense of low computational efficiency and given prior information.

Mitigating wind noise with a spherical microphone array.

This paper utilizes a rigid spherical microphone array to reduce wind noise. In the experiments conducted, a loudspeaker is used to reproduce the desired sound signal and an axial fan is employed to generate wind noise in an anechoic chamber. The sound signal and wind noise are measured separately with the spherical microphone array and analyzed in the spherical harmonic domain. The wind noise is found to be irregularly distributed in the spherical harmonic domain, distinct from the sound signal which is concentrated in the first few spherical harmonic modes. This difference is utilized to reduce wind noise without degrading the desired sound pressure level (SPL) by use of a low pass filter method in the spherical harmonic domain. Experimental results with both single-tonal and multi-tonal sound signals demonstrate that the proposed method can reduce wind noise by more than 10 dB in the frequency range below 500 Hz. The SPL of the desired sound signal can be extracted from wind noise with an error within 1.0 dB, even when the sound level is 8 dB lower than wind noise.

Multiple Sound Source Localization With Steered Response Power Density and Hierarchical Grid Refinement

Estimation of the direction-of-arrival (DOA) of sound sources is an important step in sound field analysis. Rigid spherical microphone arrays allow the calculation of a compact spherical harmonic representation of the sound field. The standard method for analyzing sound fields recorded using such arrays is steered response power (SRP) maps wherein the source DOA can be estimated as the steering direction that maximizes the output power of a maximally directive beam. This approach is computationally costly since it requires steering the beam in all possible directions. This paper presents an extension to SRP called steered response power density (SRPD) and an associated, signal-adaptive search method called hierarchical grid refinement for reducing the number of steering directions needed for DOA estimation. The proposed method can localize near-coherent as well as incoherent sources while jointly providing the number of prominent sources in the scene. It is shown to be robust to reverberation and additive white noise. An evaluation of the proposed method using simulations and real recordings under highly reverberant conditions as well as a comparison with the state-of-the-art methods are presented.

Nonsingular EB-ESPRIT for the localization of early reflections in a room

The eigenbeam-ESPRIT (EB-ESPRIT) can directly identify the direction of arrivals (DoAs) of sound sources through the parametric estimation process. This parametric estimation is beneficial for identifying directions of early echoes in an enclosed space, because it does not need an extra peak searching step for finding dominant peak locations from a beamforming power map. Nevertheless, the use of EB-ESPRIT for echo localization has been hindered due to its ill-conditioning problem for sources positioned near the equator of the spherical coordinates. Room reflections in a reverberant room can impinge from any direction, and hence, the ill-conditioning is highly likely to occur. In this work, a nonsingular EB-ESPRIT technique is utilized for the echo localization without the ill-conditioning problem. The technique is based on new recurrence relations of spherical harmonics that express DoA parameters in form of sinusoidal functions. Therefore, the ill-conditioning due to the use of arctangent function can be avoided. The performance is demonstrated using the room impulse responses simulated and measured for a rigid spherical microphone array. Frequency smoothing is applied to localize echoes that are highly coherent to each other, and results demonstrate that accurate localization of echoes is possible irrespective of their incidence angles.

A comparison of modal and spatially matched-filter beamforming for rigid spherical microphone arrays in the context of data-based binaural synthesis

Several approaches to data-based binaural synthesis have been published that capture a sound field by means of a spherical microphone array. The captured sound field is decomposed into plane waves, which are auralized using (far-field) head-related impulse responses (HRIRs). In practice, the decomposition into plane waves is performed by beamforming. A well-known technique for spherical microphone arrays is modal beamforming where the sound field is represented with respect to surface spherical harmonics. A numerically stable approximation is the spatio-temporal matched-filter technique. Here the acoustic reciprocity theorem is used in conjunction with the matched filter technique for beamforming. This paper reviews the matched filter beamformer and compares its properties to the modal beamformer in a realistic scenario. The performance of the two beamforming techniques is compared in the context of data-based binaural synthesis. Time-domain properties of the resulting ear-signals, as well as suitable binaural measures, are investigated for simulated and captured scenarios.

Spatial accuracy of binaural synthesis from rigid spherical microphone array recordings

Spatial accuracy of binaural synthesis from rigid spherical microphone array recordings

Source distance determination based on the spherical harmonics

This paper deals with the processing of signals measured by a spherical microphone array, focusing on the utilization of near-field information of such an array. The processing, based on the spherical harmonics decomposition, is performed in order to investigate the radial-dependent spherical functions and extract their argument – distance to the source. Using the low-frequency approximation of these functions, the source distance is explicitly expressed. The source distance is also determined from the original equation (using no approximation) by comparing both sides of this equation. The applicability of both methods is first presented in the noise-less data simulation, then validated with data contaminated by the additive white noise of different signal-to-noise ratios. Finally, both methods are tested for real data measured by a rigid spherical microphone array of radius 0.15m, consisting of 36 microphones for a point source represented by a small speaker. The possibility of determination of the source distance using low-order spherical harmonics is shown.

Sound field interpolation in the spatial domain with a rigid spherical microphone array

Sound field interpolation aims to calculate sound fields at arbitrary points from original measurements at discrete points. Rigid spherical microphone arrays are effective for interpolation because they can capture sound from several directions with uniform resolution. Interpolation from spherical array measurements is typically based on the spherical Fourier transform and assumes no prior knowledge concerning the source positions. The spherical Fourier transform, however, yields results whose accuracy strongly depends on microphone positioning and the inversion method used for its computation. When knowledge of the source positions is available, the pressure generated at any point on the rigid spherical baffle can be estimated with an existing physical model. This model was used in this study to define an analytic transfer function that relates the pressure at two arbitrary points on a rigid sphere. Based on this analytic function, an interpolation method in the spatial domain is presented as an alternative to transformed domain methods. Numerical experiments with a rigid sphere showed that accurate interpolation of magnitude and phase, over the full range of frequencies, is possible on the side of the array ipsilateral to the sound sources. However, on the contralateral side, accuracy systematically decreased as frequency increased.

Study of Spherical Near-Field Acoustic Holography with Rigid Spherical Microphone Array

The aim of this paper is to investigate the impacts of various parameters of rigid spherical microphone array in detecting and locating interior sound source. Helmholtz Equations are adopted to express the sound field produced by the incident field and scattered field. The gradient of the pressure is zero at the surface for the sphere is rigid. Both the incident and scattered coefficient could be obtained by solving the Helmholtz Equation using the boundary condition. Then the interior sound field could be detected and located on with the methodology of spherical near-field acoustic holography (SNAH). This study is developed in two aspects，one is configuring the microphone in various distribution in the same sphere radius, and the other one is changing the radius of sphere array. Numerical simulations are carried out to determine the optimum microphone array configuration and structure parameters. One, two, and three sound sources are arranged respectively in different displacement to the sphere center and in different angle direction to simulate the real situation. During the experiments, Omni-directional speakers and beeps are adopted as sound sources. The result shows that the method to detect and locate sound source in interior sound field is valid.

Vector intensity reconstructions in a volume surrounding a rigid spherical microphone array

A technique is described to image the vector intensity in the near field of a spherical array of microphones flush mounted in a rigid sphere. The spatially measured pressure is decomposed into Fourier harmonics in order to reconstruct the volumetric vector intensity outside the sphere. The theory for this reconstruction is developed in this paper. The resulting intensity images are very successful at locating and quantifying unknown exterior acoustic sources, ideal for application in noise control problems in interior spaces such as automobiles and airplanes. Arrays of varying numbers of microphones and radii are considered and compared and errors are computed for both theory and experiment. It is demonstrated that this is an ill-posed problem below a cutoff frequency depending on array design, requiring Tikhonov regularization below cutoff. There is no low frequency limit on operation, although the signal-to-noise ratio is the determining factor for high-spatial resolution at low frequencies. It is shown that the upper frequency limit is set by the number of microphones in the array and is independent of noise. The accuracy of the approach is assessed by considering the exact solution for the scattering of a point source by a rigid sphere. Several field experiments are presented to demonstrate the utility of the technique. In these experiments, the partial field decomposition technique is used and holograms of multiple exterior sources are separated and their individual volumetric intensity fields imaged. In this manner, the intensity fields of two uncorrelated tube sources in an anechoic chamber are isolated from one another and separated intensity maps are obtained from over a broad frequency range. In a practical application, the vector intensity field in the interior of an automobile cabin is mapped at the fundamental of the engine vibration using the rigid sphere positioned at the driver's head. The source regions contributing to the interior cabin noise are identified.

A comparison of measured and theoretical performance of a co‐centred rigid and open spherical microphone array

We present a comparison of the measured and theoretical performance of a dual co‐centred spherical microphone array that consists of an open spherical microphone array with a smaller, rigid spherical microphone array at its centre. The dual co‐centred spherical microphone array has 64 microphones, with 32 microphones on the open spherical microphone array of radius 6.30 cm and 32 microphones on the rigid spherical microphone array of radius 1.63 cm. We have previously shown [1] that this even distribution of microphones, between the two spherical microphone arrays, provides a greater frequency range of operation for a third‐order, 64‐channel spherical microphone array compared to a single rigid 64‐channel spherical array. The performance of the dual co‐centred spherical microphone array is measured in an anechoic chamber using a speaker mounted on a robotic arm. A comparison is made between the theoretical and measured directivity pattern for various frequencies. [1] A. Parthy, C. Jin, and A. van Schaik "Optimisation of Co‐centred Rigid and Open Spherical Microphone Arrays," in Proc. of 120th Audio Engineering Convention, Paris, France, May 20‐23, 2006.

Vector intensity measurement with a rigid spherical microphone array in a vehicle cabin

Measurement results showing intensity vector reconstructions using a rigid spherical microphone array in a vehicle cabin are presented. The measurement equipment developed by Nittobo was used in previous demonstrations to visualize the acoustic field using a beamforming technique superimposed on a picture from an on-board camera. In the present study intensity reconstructions are shown and are successful in locating and quantifying sources, demonstrating the usefulness of this technique in an enclosed space like a vehicle cabin, aircraft cabin, small room, etc. This work was supported by the US Office of Naval Research and Nittobo Acoustic Engineering Co. Ltd.