Representation Of Sound Field Research Articles

Series expansions of rotating two and three dimensional sound fields

The cylindrical and spherical harmonic expansions of oscillating sound fields rotating at a constant rate are derived. These expansions are a generalized form of the stationary sound field expansions. The derivations are based on the representation of interior and exterior sound fields using the simple source approach and determination of the simple source solutions with uniform rotation. Numerical simulations of rotating sound fields are presented to verify the theory.

Plane-Wave Decomposition of Acoustical Scenes Via Spherical and Cylindrical Microphone Arrays

Spherical and cylindrical microphone arrays offer a number of attractive properties such as direction-independent acoustic behavior and ability to reconstruct the sound field in the vicinity of the array. Beamforming and scene analysis for such arrays is typically done using sound field representation in terms of orthogonal basis functions (spherical/cylindrical harmonics). In this paper, an alternative sound field representation in terms of plane waves is described, and a method for estimating it directly from measurements at microphones is proposed. It is shown that representing a field as a collection of plane waves arriving from various directions simplifies source localization, beamforming, and spatial audio playback. A comparison of the new method with the well-known spherical harmonics based beamforming algorithm is done, and it is shown that both algorithms can be expressed in the same framework but with weights computed differently. It is also shown that the proposed method can be extended to cylindrical arrays. A number of features important for the design and operation of spherical microphone arrays in real applications are revealed. Results indicate that it is possible to reconstruct the sound scene up to order p with p2 microphones spherical array.

Synthesis of Room Responses Using the Virtual Source Representation and the Comb-Nested Allpass Filters

Abstract An artificial reverberator is proposed in this paper to synthesize room responses. The method employs the virtual source representation and the comb-nested allpass filters to generate the early reflection and late reverberation, respectively, of room responses. The virtual source method is based on a simple representation of sound field with a distribution of discrete simple sources on the boundary. The complex strengths of the virtual sources are then calculated by solving a frequency domain least-square problem. Parameters such as room geometry, size, and wall absorption are naturally incorporated into the synthesis process. The filtering property of human hearing is also exploited in a nonuniform sampling procedure to further simplify the computation. Apart from the early reflection, a comb-allpass filter network is adopted to simulate late reverberations. Optimal parameters of the comb-allpass filter network are obtained using the genetic algorithm (GA). The energy decay curve (EDC) is chosen as the objective function in the GA procedure. Numerical simulations are carried out for a rectangular room and a concert hall model to verify the proposed technique. Subjective listening experiments demonstrate that the present technique is capable of conferring remarkable realism of room responses.

Impulse Representation of Sound Field due to a Rigid Wedge

An impulse representation for calculating a diffraction wave due to a rigid wedge is described. The method is an approximation of the Biot-Tolstoy rigorous closed-form solution for the diffraction of point source radiation by an infinite rigid wedge. The band-limited time-domain function can be reconstructed to the original waveform if it satisfies the sampling theorem, which assumes that sampling takes place at the lowest permissible sampling rate. Therefore, if the energy is concentrated between the first sampling intervals immediately after the rise time of the time-domain function, the rigorous solution can be approximated as a delta function. This paper shows the description methods of the diffraction field near the ridge in three-dimensional space. Using the proposed impulse representation, numerical simulation was performed and the calculation accuracy was examined.

Adaptive Multigrid for Helmholtz Problems

Solving Helmholtz problems for low frequency sound fields by a truncated modal basis approach is very efficient. The most time-consuming process is the calculation of the undamped modes. Using traditional FE solvers, the user has to provide a mesh which has at least six nodes per wavelength in each spatial direction to achieve acceptable results. Because the mesh size increases with the 3rd power of the highest frequency of interest, this uniform dense mesh approach is a very expensive way of creating a modal space. However, the number of modes and the accuracy of the modal basis directly influences the solution quality. It is well known that the representation of sound fields by modal basis functions φi is optimal with respect to the L2 error norm. This means that having a modal basis Φ := {φi, i = 1⋯n}, the distance between true and approximated sound field takes its minimum in the mean square. So, it is necessary to have a FE basis which also minimizes the discretization error when computing the modal basis. One can reach this goal by applying adaptive mesh refinements. Additionally, this yields the opportunity of using fast multigrid methods to solve discrete eigenvalue problems. In context of this presentation we will discuss the results of our adaptive multigrid algorithms.

P1-A-3 Numerical Analysis of Impulsive Representation of Sound Field Near the Ridge of a Wedge

P1-A-3 Numerical Analysis of Impulsive Representation of Sound Field Near the Ridge of a Wedge

Sound field representation by virtual potential near apex and its application to boundary value problem

A new scheme for representing 2D sound field diffracted by a rigid polygon is proposed where the sound field is described by a sum of two potentials, that is, one that depends on the geometrical arrangement of a point source, an observation point and the polygon and the other that depends on the contribution from the potential at the surface of the scatterer. The latter potential is calculated by assuming virtual potentials in the vicinity of every apex of the polygon and the sound field is calculated using the virtual potential even in the vicinity of the apex using virtual discontinuity principle of diffraction that has been proposed by us before. The virtual potential is fixed so that the calculated potential is continuous across the apex. Consequently two sampling points are necessary in the vicinity of every apex to assure the continuity of the potential across the apex. Thus, the total number of sampling points can be reduced remarkably in this new method. The new method is applied to a semi-infinite plane and a strip and the estimated boundary values are compared with rigorous solutions. Remarkably good agreements are obtained using few sampling points.

Extension of the Huygens–Fresnel principle to a virtual space

The quantitative description of diffraction started with Fresnel, who introduced the interference effect to Huygens’ principle where diffracted waves are expressed by an integral of secondary wavelets over an opening in an opaque screen. Although this diffraction formula is an approximate one, it has given precise estimation of waves diffracted by the opening. Most diffraction phenomena arise from 3-D objects. However, attempts to apply the diffraction theory to 3-D objects are unsuccessful since, in these cases, the region for integration of secondary wavelets cannot be determined clearly. In order to explain the diffraction by polyhedrons, a hypothetical observer is assumed at an observation point and the Huygens–Fresnel principle is extended to a space seen by the observer virtually. In this virtual space the observer can see real images and mirror images through facets of the polyhedron and every point in real and mirror images is considered as a center of the secondary wavelets. The new representation of sound field diffracted by 3-D objects that satisfies both the wave equation and boundary conditions is derived by this extension [J. Acoust. Soc. Am. 95, 2354–2362 (1994)]. The algorithm to obtain solutions from this representation will be discussed in detail.

Modal analysis techniques applied to sound field representation

In structural dynamics, modal analysis permits normal mode representation for vibrating structures by recording multiple transfer functions and letting a computer animate a simple harmonic oscillator approximation to display normal mode motion in an expanded time frame. This work shows an example of applying this technique to the representation of a sound field. Phase information is recorded by using the excitation source as a reference signal, monitoring the sound field with a microphone, and forming a transfer function of the two with a dual channel FFT analyzer. The method is illustrated by showing the sound field above and below the sound board of a grand piano, and in a vertical plane in the general direction of an audience.

IMPROVED SUPPRESSION OF UNCORRELATED BACKGROUND NOISE WITH THE STSF TECHNIQUE

The Spatial Transformation of Sound Fields (STSF) technique permits a 3D sound field mapping based on a 2D scan measurements in the near field of a source. By measurement of the cross spectra between a set of references and the cross spectra from each scan position to each of the references, a principal component representation of the sound field is extracted which can be applied for near field holography and Helmholtz' integral equation calculations. Basically, this sound field representation includes only the part of the sound field, which is coherent with the reference signals. More precisely, only views of the independent parts of the sound field seen by the references are included. Therefore, provided the references do not pick up the background noise, the background noise will not be part of the sound field model processed by STSF. However, if the background noise is picked up by the reference transducers, it will become part of the model and cause errors in the calculations. In order to overcome this problem, the possibility of using a set of exclude references has been implemented in the STSF system. These references should pick up only the uncorrelated background noise to be suppressed in the model

Scattering−matrix description and nearfield measurements of electroacoustic transducers

Recently developed and successfully applied analytical techniques for the measurement of microwave antennas at reduced distances are ’’translated’’ into corresponding techniques for the measurement of electroacoustic transducers in fluids. The basic theory is formulated in scattering−matrix form and emphasizes the use of plane−wave spectra for the representation of sound fields. This theory, in contrast to those based on asymptotic description of transducer characteristics, is suitable for the formulation and solution of problems involving interactions at arbitrary distances. Two new techniques (in particular) are described. One, utilizing deconvolution of transverse scanning data, taken with a known tranducer at distances d which may be much less than the Rayleigh distance dR(≡ D2/2), provides a means of obtaining complete near− and farfield characteristics, corrected for the effects of the measuring transducer. Applicability of a (two−dimensional, spatial) sampling theorem and the ’’fast Fourier transform’’ algorithm, which greatly facilitate the necessary computations, is shown. The second technique provides a means of extrapolating received signal as a function of distance (observed with d ∠ dR) to obtain on−axis values of effective directivity. Other possible applications are indicated. These techniques rigorously utilize observed transducer output, which need not be simply related to pressure or normal velocity at a point. Subject Classification: 85.40, 85.62; 30.85.

Scattering-Matrix Description and Nearfield Measurements of Electroacoustic Transducers

Recently developed analytical techniques for the measurement of microwave antennas at reduced distances are “translated” into corresponding techniques for the measurement of electroacoustic transducers in fluids. The basic theory is formulated in scattering-matrix form and emphasizes the use of plane-wave spectra for the representation of sound fields. This theory, in contrast to those based on asymptotic description of transducer characteristics, is suitable for the formulation and solution of problems involving interactions at arbitrary distances. Two new techniques (in particular) are described: One, utilizing deconvolution of transverse scanning data, which may be taken at distances d much less than the Rayleigh distance dR(≡ a2/2λ), provides a means of obtaining complete effective directivity functions, corrected for the effects of the measuring transducer. Applicability of a (two-dimensional, spatial) sampling theorem and the “fast Fourier transform” algorithm, which greatly facilitate the necessary computations, is shown. The second technique provides a means of extrapolating received signal as a function of distance (observed with d∼dR or d≫a instead of the conventional d∼dR) to obtain on-axis values of effective directivity. Other possible applications are indicated. In these techniques, pressure data are rigorously sufficient; normal velocity data are not required.