Rigid Spherical Array Research Articles

Multichannel Blind Source Separation Based on Evanescent-Region-Aware Non-Negative Tensor Factorization in Spherical Harmonic Domain

There is growing interest in new audio formats in the context of virtual reality (VR), and higher-order ambisonics (HOA) is preferred for VR systems to transmit recorded scenes owing to its transmission efficiency and its flexibility to work with different loudspeaker setups. However, the conversion between another well-known format, i.e., object format, and the HOA format is not fully addressed in the literature. To address this issue, blind source separation in a spherical harmonic (SH) domain can be considered as the best way to extract objects in terms of efficiency, i.e., decoding HOA signals for separation can be omitted. A few authors attempted to extract objects from encoded HOA signals directly by using multichannel non-negative matrix factorization (MNMF), but these approaches either assume only far-field sources or do not take array characteristics into account, which make these methods difficult to use for VR in practical situations where singers or speakers often perform close to microphones. Furthermore, MNMF generally requires a huge computational cost, although dimensional reduction to the SH domain is performed. In this work, we also model near-field sources by estimating the model parameters of non-negative tensor factorization (NTF) in the SH domain assuming that microphone signals can be obtained with a rigid spherical array. We propose a masking scheme to exclude noisy evanescent regions in the SH domain from the NTF cost function. Evaluations show that our method outperforms existing methods devised for the HOA format and that our masking approach is effective in improving the separation quality.

Comparison of two microphone array geometries for surface impedance estimation.

This study examines the estimation of the surface impedance of an absorber with microphone arrays. Two array geometries are compared-a rigid spherical array and a double layer planar array. The impedance is estimated via reconstructing the sound field (pressure and particle velocity) on the absorber's surface, using a plane wave expansion. The comparison is carried out by studying the numerical properties of the two arrays as well as through experimental tests.

Wideband holography based spherical equivalent source method with rigid spherical arrays

Abstract Spherical equivalent source method (S-ESM) with rigid spherical arrays is able to achieve good sound field reconstruction and acoustic source identification in three-dimensional free-field spaces. However, the S-ESM solved by the standard Tikhonov regularization is restricted to the low-frequency reconstruction and source identification at small measurement distances. To make S-ESM achieve good reconstruction and source identification at high frequencies and large hologram distances, this study proposes a sparsity-promoting approach denoted as wideband holography based S-ESM (WBH-based S-ESM), which applies a steepest descent method to iteratively solve S-ESM. Firstly, the framework of WBH-based S-ESM is established. Subsequently, to examine its validity, the performance of reconstruction and source identification is compared with Tikhonov regularization. Finally, a focus is concerned with the adaptability to large hologram distances. Several meaningful results have emerged from simulations and experiments: (1) WBH-based S-ESM can make good sound field reconstruction and acoustic source identification at medium-high frequencies. It extends the upper frequency limit of S-ESM. (2) The maximum hologram distance of WBH-based S-ESM at high frequencies is greater than that of Tikhonov regularization. It enlarges the measurement distance of S-ESM. This study will demonstrate the potential of WBH-based S-ESM as a useful tool for reconstruction and source identification.

Spherical beamforming for spherical array with impedance surface

Spherical microphone array beamforming has been a popular research topic for recent years. Due to their isotropic beam in three dimensional spaces as well as a certain frequency range, the arrays are widely used in many applications such as sound field recording, acoustic beamforming, and noise source localisation. The body of a spherical array is usually considered perfectly rigid. A sound field captured by the sensors on spherical array can be decomposed into a series of spherical harmonics. In noise source localisation, the amplitude density of sound sources is estimated and illustrated by mean of colour maps. In this work, a rigid spherical array covered by fibrous materials is studied via numerical simulation and the performance of the spherical beamforming is discussed.

Estimation of surface impedance using different types of microphone arrays

This study investigates microphone array methods to measure the angle dependent surface impedance of acoustic materials. The methods are based on the reconstruction of the sound field on the surface of the material, using a wave expansion formulation. The reconstruction of both the pressure and the particle velocity leads to an estimation of the surface impedance for a given angle of incidence. A porous type absorber sample is tested experimentally in anechoic conditions for different array geometries, sample sizes, incidence angles, and distances between the array and sample. In particular, the performances of a rigid spherical array and a double layer planar array are examined. The use of sparse array processing methods and conventional regulariation approaches are studied. In addition, the influence of the size of the sample on the surface impedance estimation is investigated using both experimental data and numerical simulations with a boundary element model. Results indicate that the small distance b...

Sound field reconstruction using a spherical microphone array.

A method is presented that makes it possible to reconstruct an arbitrary sound field based on measurements with a spherical microphone array. The proposed method (spherical equivalent source method) makes use of a point source expansion to describe the sound field on the rigid spherical array, from which it is possible to reconstruct the sound field over a three-dimensional domain, inferring all acoustic quantities: sound pressure, particle velocity, and sound intensity. The problem is formulated using a Neumann Green's function that accounts for the presence of the rigid sphere in the medium. One can reconstruct the total sound field, or only the incident part, i.e., the scattering introduced by the sphere can be removed, making the array virtually transparent. The method makes it possible to use sequential measurements: different measurement positions can be combined, providing an extended measurement area consisting of an array of spheres, and the sound field at any point of the source-free domain can be estimated, not being restricted to spherical surfaces. Because it is formulated as an elementary wave model, it allows for diverse solution strategies (least squares, ℓ1-norm minimization, etc.), revealing an interesting perspective for further work.

Optimal Real-Weighted Beamforming With Application to Linear and Spherical Arrays

One of the uses of sensor arrays is for spatial filtering or beamforming. Current digital signal processing methods facilitate complex-weighted beamforming, providing flexibility in array design. Previous studies proposed the use of real-valued beamforming weights, which although reduce flexibility in design, may provide a range of benefits, e.g., simplified beamformer implementation or efficient beamforming algorithms. This paper presents a new method for the design of arrays with real-valued weights, that achieve maximum directivity, providing closed-form solution to array weights. The method is studied for linear and spherical arrays, where it is shown that rigid spherical arrays are particularly suitable for real-weight designs as they do not suffer from grating lobes, a dominant feature in linear arrays with real weights. A simulation study is presented for linear and spherical arrays, along with an experimental investigation, validating the theoretical developments.

Experimental investigation on reconstruction of sound field based on spherical near-field acoustic holography

This paper presents the results of an experimental study on the methodology of spherical near-field acoustic holography (spherical NAH) to reconstruct interior sound field. The experiment was carried out in a full anechoic chamber, in which the sound filed was generated with different combination of speakers at different positions, a rigid spherical array was used to collect the field acoustic pressures as input to the reconstruction calculation. There are three cases which were investigated. Case 1, a source was set near to the microphone array. Case 2, two sources were eccentrically set opposite to each other around the microphone array. And Case 3, two sources were placed on one side of microphone array on the same orbit, while they were positioned apart at a small angle. The accuracy of the reconstruction of sound field was examined and analyzed compared to the benchmarks and the results of the numerical simulations. The reconstructed results show that the methodology of Spherical NAH is capable to locate sources and reconstruct sound field within certain accuracy.

Interior holography.

Interior spaces with vibrating walls embrace a broad set of structural acoustic problems (planes, trains and automobiles). In the hunt for efficient measurement schemes that provide details of both the acoustic and structural fields, inverse holographic methods are very promising. These methods use a surface of measured data and mathematically back-track the field in time and space filling in a 3-D volume around the array in the process and are particularly attractive since they can image the time averaged acoustic intensity vector, localizing and quantifying surface sources. There is a score of holographic back-propagation methods in use today. In almost all cases single measurement surfaces are not accurate due to reverberation and dual conformal surfaces are needed to separate sound fields coming from forward and backward directions. The spherical array (open or rigid) is a noticeable exception, an accurate mathematical approach is obtained with only one surface of data. This paper presents an overview of the inverse problem in interior spaces paying particular attention to the rigid spherical array, discussing improvements that extend the frequency range and volume of study, and simple regularization methods to stabilize the ill-posed nature of the volumetric reconstructions. [Work supported by ONR.]

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

An approach is presented that provides a prediction of the vector intensity field throughout a volume exterior to a rigid spherical measurement array consisting of 31 flush mounted microphones. The theory is based on spherical harmonic expansions of the measured field with the radial variation of the near-field pressure obtained using the Greens function with vanishing normal derivative at the rigid sphere surface. Experimental results with rigid spherical arrays of differing radii are presented using multiple incoherent sources. Successful intensity reconstructions are obtained over a volume three times the sphere radius up to a frequency of 1.5 kHz that clearly reveal the locations and levels of the two sources. This volumetric intensity probe is very similar mathematically to one described recently by the author (EGW) that used 50 microphones in an open array. The latter was used successfully inside an aircraft cabin in flight to uncover sources of noise. This work was supported by the US Office of Naval Research and Nittobo Acoustic Engineering Co. Ltd.

3D localization of acoustic sources with a spherical array

This paper describes a technique dedicated for the localization of acoustic sources in all directions and in the far-field. Classical beamforming techniques based on planar arrays provides an acoustic map restricted to a limited aperture, but a spherical array does not have such a limitation since there is no preferential direction. In this processing called Spherical Harmonics Beamforming, the sound field on the sphere is decomposed with spherical harmonics functions, and then a corrected summation gives the acoustic contribution from a given direction. We have used a rigid spherical array, which has the advantage that cabling of microphones and integrated cameras can be hidden inside the sphere. A rigid surface also provides better numerical stability in connection with Spherical Harmonics Beamforming. In this study, this technique is evaluated in connection with the resolution and the dynamic range. Simulated and experimental results are presented.