Representation Of Sound Field Research Articles

A novel numerical method for solving the Kirchhoff-Helmholtz integral equation based on the sound field representation using the reproducing kernel in the frequency domain

The paper introduces a unique numerical solution method for the Kirchhoff-Helmholtz integral equation. This method is based on the representation of the sound field using the reproducing kernel in the solution space of the homogeneous Helmholtz equation. When compared to the conventional boundary element method, the proposed method holds numerous advantages. This paper presents the analysis theory of the proposed method and demonstrates its validity by calculating bounded and unbounded sound fields. The accuracy of the calculation is assessed by computing the sound field in a rectangular room under various conditions. Furthermore, although some theoretical issues remain, the proposed method effectively avoids the non-uniqueness of solutions in unbounded domain problems.

Estimation of the surface impedance based on the discrete complex image source method and array processing

This paper introduces a method for estimating the sound absorption coefficient of a large panel of absorbing material from measurements using a microphone array. The method relies upon describing the pressure field as the set of monopoles obtained when the reflection coefficient is represented as the Laplace Transform of an image source distribution. This formulation results in a well-behaved integral equation, which is discretized using Gaussian quadrature to yield an inverse problem. It is possible to determine the regularized solution to the inverse problem and reconstruct the surface impedance of the sample by conducting measurements of the sound pressure at multiple points of observation. This sound field representation is adequate for sound sources in the close range of the material and the array. The paper presents simulated and experimental investigations to delineate the efficacy of the proposed measurement technique against the well-known image source method, thereby highlighting its significant potential to advance acoustic characterization methodologies.

Phase space representation of sound field excited by a noise source in underwater acoustic waveguide.

The analysis of the field excited in a waveguide by a point noise source is performed using the phase space representation of this field given by the distribution of its amplitude in the depth-angle-time space. The transition from the traditional description of the field amplitude as a function of depth and time to phase space representation is performed using the coherent state expansion developed in quantum mechanics. In this paper, the correlation function of noise signals arriving at different points of the phase plane depth-angle is investigated. Numerical simulation data show that measurements of signal correlations in phase space, performed with the help of a receiving vertical antenna, can be used as input data in solving the problem of source localization and reconstruction of unknown parameters of the sound speed profile. It is shown that in phase space there is an analog of the classical interference pattern observed in the distribution of sound intensity in the distance-frequency plane. The slopes of striations in this interference pattern, as in the conventional one, are given by the Chuprov waveguide invariant.

Phase Space Representation of Sound Fields in Lake Kinneret

Phase Space Representation of Sound Fields in Lake Kinneret

Synthesis of sound field from moving complex sources with arbitrary trajectories by linear and spherical loudspeaker arrays.

The spectral division method (SDM) and near-field compensated higher order ambisonics (NFC-HOA) are sound field synthesis techniques based on the spatial Fourier representation of sound fields. Previous studies have derived the driving functions of SDM for sound field synthesis with consideration to uniformly moving point sources and moving point sources with arbitrary trajectories. However, the driving functions of NFC-HOA for synthesizing sound fields from moving sound sources have not been proposed to date. For a more realistic auditory experience, the synthesis of a sound field produced by a moving sound source with a complex radiation property is required. This study focused on deriving the driving functions for synthesizing sound fields produced by moving sound sources with arbitrary trajectories and radiation properties. Sound fields were formulated in the angular spectrum and spherical harmonic domains and applied to SDM and NFC-HOA, respectively. Numerical and measurement experiments were conducted to evaluate the proposed method. The results reveal that the proposed method can synthesize the desired sound fields.

Dual quaternion ambisonics array for six-degree-of-freedom acoustic representation

Spatial audio methods are gaining a growing interest due to the spread of immersive audio experiences and applications, such as virtual and augmented reality. For these purposes, 3D audio signals are often acquired through arrays of Ambisonics microphones, each comprising four capsules that decompose the sound field in spherical harmonics. In this paper, we propose a dual quaternion representation of the spatial sound field acquired through an array of two First Order Ambisonics (FOA) microphones. The audio signals are encapsulated in a dual quaternion that leverages quaternion algebra properties to exploit correlations among them. This augmented representation with 6 degrees of freedom (6DOF) involves a more accurate coverage of the sound field, resulting in a more precise sound localization and a more immersive audio experience. We evaluate our approach on a sound event localization and detection (SELD) benchmark. We show that our dual quaternion SELD model with temporal convolution blocks (DualQSELD-TCN) achieves better results with respect to real and quaternion-valued baselines thanks to our augmented representation of the sound field. Full code is available at: https://github.com/ispamm/DualQSELD-TCN.

Tensor dictionary learning for representing three-dimensional sound speed fields.

Ocean sound speed field (SSF) representation is often plagued with low resolution (i.e., the capability of explaining fine-scale fluctuations). This drawback, however, is inherent in a number of classical SSF basis functions, e.g., empirical orthogonal functions, Fourier basis functions, and more recent tensor-based basis functions learned via the higher-order orthogonal iterative algorithm. For two-dimensional depth-time SSF representation, recent attempts relying on dictionary learning have shown that fine-scale sound speed information can be well preserved by a large number of basis functions. They are learned from the historical data without imposing rigid constraints on their shapes, e.g., the orthogonal constraints. However, generalizing the dictionary learning idea to represent three-dimensional (3D) spatial ocean SSF is non-trivial, in terms of both problem formulation and algorithm development. It calls for integrating the dictionary learning framework and the tensor-based basis function learning framework, a recently proposed one that captures the 3D sound speed correlations well. To achieve this goal, we develop a 3D SSF-tailored tensor dictionary learning algorithm that learns a large number of tensor-based basis functions with flexible shapes in a data-driven fashion. Numerical results based on the South China Sea 3D SSF data have showcased the superiority of the proposed approach over the prior method.

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.

Spherical sector harmonics representation of sound fields using a microphone array over spherical sector.

Spherical microphone arrays (SMAs) are widely used for sound recording and analysis, with processing being done in the spherical harmonics (SH) domain. This is due to the ease of array processing in the SH domain without spatial ambiguity. However, it is uneconomical to construct a full SMA when sources are present in restricted regions of the environment. Additionally, the use of a full SMA comes at the cost of more microphone signals to process. Attempts have been made to use hemispherical microphone arrays on the basis of the acoustic image principle, enabling application of SH but with greater computational complexity. In this paper, the use of a spherical sector microphone array instead of a full SMA is proposed. An orthonormal spherical sector harmonics (S2H) basis function is developed for accurate representation of pressure over the sector. The orthonormality of the S2H function is established using orthogonality of shifted associated Legendre polynomials and a scaled exponential function. An addition theorem for S2H basis functions is derived. The S2H basis function is applied to the decomposition of a sound field over a sector array. The S2H basis function has potential applications to brain source localization and physiological shape description.

Validation and application of three-dimensional auralisation during concert hall renovation

During the renovation of auditoria and concert halls, the acoustic quality is normally evaluated from measurements of impulse responses. One possibility for evaluating the acoustic quality from the measurements (the simulations) consists of convolving anechoic music with the measured (or simulated) impulse responses. In this way, a psycho-acoustic test is achieved using a virtual sound field representation. The listening room ‘Arlecchino’ at the University of Bologna includes ambisonics (up to fifth order) and stereo-dipole playback for virtual reproduction of sound in rooms. In this article, the effectiveness of the listening room ‘Arlecchino’ is first analysed, comparing acoustic parameters obtained from binaural impulse responses measured in some opera houses (in Italy) and auditorium (in Japan) with those virtually measured after the virtual reconstruction obtained in the listening rooms. The similarity between real and virtual sound fields, has been evaluated by comparing different acoustic parameters calculated by real and virtual sound fields, in four halls in different configurations, by means of the stereo-dipole method. In the second part of the article, the listening room was used to analyse the variation in interaural cross-correlation measurements in rooms obtained considering different anechoic sound signals convolved with the binaural impulse responses, to quantify the variation of the interaural cross correlation with different motifs. For this purpose, two different musical instrument digital interface musical motifs, very different from each other for their music characteristics, have been considered. Moreover, for each musical motif, different sound characteristics (i.e. different musical instruments) were considered, to consider both the rhythmic and timbre aspect.

Characterization of acoustic material at oblique incidence using a spherical microphone array.

This paper proposes two distinct methods for estimating the surface impedance Zs of acoustic materials using a spherical microphone array. The first method is based on the spherical ambisonic representation of sound fields to estimate the normal particle velocity and the sound pressure at the surface of the material. The second method uses an optimization process, where the measured sound pressure field is constrained to match a theoretical model. These two methods are compared to two existing methods: the equivalent source approach and the two-microphone measurement technique. The results show a clear advantage of the microphone array methods compared to the classical two-microphone method. The measurements show an accurate reconstruction of surface impedance and absorption coefficient between 120 and 5000 Hz for various sound incidences but also show edge effect perturbations due to the limited size of the tested samples. In addition, two criteria are proposed, one estimating the noise floor level allowing the optimization of the measurement results, the other evaluating the area of accurate impedance reconstruction on the surface of the material.

Spherical harmonic representation of rectangular domain sound fields

Spherical harmonic representation of rectangular domain sound fields

Sound field reconstruction using multipole equivalent source model with un-fixed source locations.

The equivalent source methods (ESM) that have been developed to this point can generally be classified into two categories: one in which a relatively large number of lower order sources are fixed at various locations, and one in which a series of higher order sources are fixed at one location. The present work started with a model in the latter category, but the individual sources were then allowed to move separately to locations which were determined by using a nonlinear optimization procedure based on the measured sound field data. To test this approach, experiments were conducted using a small loudspeaker cabinet; measurements were made using an array of microphones on all sides of the loudspeaker. It was found that by allowing the source components to move, the sound field representation in both the near and far fields was improved, particularly at high frequencies, compared to the model with fixed source locations. By comparison with results obtained from boundary element calculations based on laser vibrometer measurements of the loudspeaker's diaphragm and tweeter velocities, it was found that the proposed ESM can also be used to accurately predict the sound pressure distribution on the source surface.

スパース音場表現に基づく超解像型収音・再現( スパース表現に基づく音響信号処理)

スパース音場表現に基づく超解像型収音・再現( スパース表現に基づく音響信号処理)

Low Frequency Interactive Auralization Based on a Plane Wave Expansion

This paper addresses the problem of interactive auralization of enclosures based on a finite superposition of plane waves. For this, room acoustic simulations are performed using the Finite Element (FE) method. From the FE solution, a virtual microphone array is created and an inverse method is implemented to estimate the complex amplitudes of the plane waves. The effects of Tikhonov regularization are also considered in the formulation of the inverse problem, which leads to a more efficient solution in terms of the energy used to reconstruct the acoustic field. Based on this sound field representation, translation and rotation operators are derived enabling the listener to move within the enclosure and listen to the changes in the acoustic field. An implementation of an auralization system based on the proposed methodology is presented. The results suggest that the plane wave expansion is a suitable approach to synthesize sound fields. Its advantage lies in the possibility that it offers to implement several sound reproduction techniques for auralization applications. Furthermore, features such as translation and rotation of the acoustic field make it convenient for interactive acoustic renderings.

Extraction of Acoustic Sources Through the Processing of Sound Field Maps in the Ray Space

Our goal is to develop a model-based approach to acoustic source extraction from microphone array data, which is suitable for both near-field and far-field sources. A signal representation based on plane-wave (PW) decomposition is suitable for acoustic sources in the far field as the resulting spectrum turns out to be impulsive. When the source approaches the array, however, the curvature of the wavefront causes the spectrum of the PW components to depart from impulsive behavior, thus making source extraction harder to attain. In this paper, we adopt a sound field representation based on the local estimation of the plenacoustic function along the array line. This approach consists of dividing the array into subarrays, and applying the PW analysis on individual subarrays. This has the immediate result of extending the range of validity of the far-field hypothesis, as a source that enters the near-field range of the extended array is still in the far-field range of the subarrays. PW analysis on subarrays allows us to construct the so-called sound field map in a domain of acoustic visibility called ray space. The extraction of the desired source is accomplished through spatial filtering of the sound field map. The design of the spatial filter relies on a linear minimum mean square error criterion defined on the sound field map. The effectiveness of the proposed methodology is proven through an extensive simulation campaign as well as real experiments.

Visualizing sound directivity via smartphone sensors

We present a fast, simple method for automated data acquisition and visualization of sound directivity suitable for use with introductory acoustics education, made convenient and accessible via a new free smartphone app, “Polar Pattern Plotter.” The app synchronizes measurements of sound volume with the phone's angular orientation, obtained from either compass, gyroscope, or accelerometer sensors, and produces a graph and exportable data file. It is generalizable to various sound sources and receivers via the use of an input-jack-adaptor to supplant the smartphone's (omnidirectional) microphone. We show results obtained in a free-field environment for loudspeaker directivity, microphone polar patterns, and two-speaker interference effects. Results provide both a visual and quantitative representation of sound fields and device responses, useful for introductory acoustics experiments and demonstrations.

Fast wideband acoustical holography.

Patch near-field acoustical holography methods like statistically optimized near-field acoustical holography and equivalent source method are limited to relatively low frequencies, where the average array-element spacing is less than half of the acoustic wavelength, while beamforming provides useful resolution only at medium-to-high frequencies. With adequate array design, both methods can be used with the same array. But for holography to provide good low-frequency resolution, a small measurement distance is needed, whereas beamforming requires a larger distance to limit sidelobe issues. The wideband holography method of the present paper was developed to overcome that practical conflict. Only a single measurement is needed at a relatively short distance and a single result is obtained covering the full frequency range. The method uses the principles of compressed sensing: A sparse sound field representation is assumed with a chosen set of basis functions, a measurement is taken with an irregular array, and the inverse problem is solved with a method that enforces sparsity in the coefficient vector. Instead of using regularization based on the 1-norm of the coefficient vector, an iterative solution procedure is used that promotes sparsity. The iterative method is shown to provide very similar results in most cases and to be computationally much more efficient.

Personal Sound Zones: Delivering interface-free audio to multiple listeners

Sound rendering is increasingly being required to extend over certain regions of space for multiple listeners, known as personal sound zones, with minimum interference to listeners in other regions. In this article, we present a systematic overview of the major challenges that have to be dealt with for multizone sound control in a room. Sound control over multiple zones is formulated as an optimization problem, and a unified framework is presented to compare two state-of-the-art sound control techniques. While conventional techniques have been focusing on point-to-point audio processing, we introduce a wave-domain sound field representation and active room compensation for sound pressure control over a region of space. The design of directional loudspeakers is presented and the advantages of using arrays of directional sources are illustrated for sound reproduction, such as better control of sound fields over wide areas and reduced total number of loudspeaker units, thus making it particularly suitable for establishing personal sound zones.

Analysis of truncation and sampling errors in the spherical harmonic representation of soundfields

The use of microphone arrays to record soundfields for subsequent immersive reproduction, real time or off-line beamforming applications are becoming increasingly prevalent. The representation and analysis of such recorded soundfields using finite-order spherical harmonic coefficients is elegant and has a number of advantages. The focus of this paper is to quantify the accuracy of such a representation which is limited by errors introduced by several types of non-idealities: manufacturing non-idealities of the array such as microphone positional errors, coupling between microphones, etc.; physical non-idealities due to the discrete spatial sampling of the soundfield which introduces spatial aliasing and the inherent truncation of the modal representation of the soundfield to a finite order; and mathematical errors due to the computational technique used to derive the modal coefficients. This paper investigates the latter two classes of errors and quantifies the significant advantages in accuracy achievable when the physical structure of the microphone array allows the use of the orthogonal properties of the spherical harmonic basis functions to extract the modal coefficients. In addition, we extend previously published analysis of the truncation error, which was limited to incident plane waves, to spherical waves.