The theory of recording and reproduction of three-dimensional sound fields based on spherical harmonics is reviewed and extended. Free-field, sphere, and general recording arrays are reviewed, and the mode-matching and simple source approaches to sound reproduction in anechoic environments are discussed. Both methods avoid the need for both monopole and dipole loudspeakers—as required by the Kirchhoff–Helmholtz integral. An error analysis is presented and simulation examples are given. It is also shown that the theory can be extended to sound reproduction in reverberant environments.

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Three-Dimensional Surround Sound Systems Based on Spherical Harmonics

Binaural Cue Coding (BCC) is a method for multichannel spatial rendering based on one down-mixed audio channel and side information. The companion paper (Part I) covers the psychoacoustic fundamentals of this method and outlines principles for the design of BCC schemes. The BCC analysis and synthesis methods of Part I are motivated and presented in the framework of stereophonic audio coding. This paper, Part II, generalizes the basic BCC schemes presented in Part I. It includes BCC for multichannel signals and employs an enhanced set of perceptual spatial cues for BCC synthesis. A scheme for multichannel audio coding is presented. Moreover, a modified scheme is derived that allows flexible rendering of the spatial image at the receiver supporting dynamic control. All aspects of complete BCC encoder and decoder implementations are discussed, such as down-mixing of the input signals, low complexity estimation of the spatial cues, and quantization and coding of the side information. Application examples are given and the performance of the coder implementations are evaluated and discussed based on subjective listening test results.

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Binaural cue coding-Part II:Schemes and applications

The Sonification Handbook

Transfer-function measurements using sweeps as excitation signals rather than pseudonoise signals show significantly higher immunity against distortion and time variance. Capturing binaural room impulse responses for high-quality auralization purposes requires a signal-to-noise ratio (SNR) greater than 90 dB, which is unattainable with maximum-length sequence (MLS) measurements because of loudspeaker nonlinearity, but it is fairly easy to reach with sweeps due to the possibility of complete rejection of harmonic distortion. Before investigating the differences and practical problems of measurements with MLS and sweeps and arguing why sweeps are the preferable choice for the majority of measurement tasks, the existing methods of obtaining transfer functions are reviewed. The continual need to use preemphasized excitation signals in acoustical measurements is also addressed. A method to create sweeps with arbitrary spectral contents, but constant or prescribed frequency-dependent temporal envelope, is presented. Finally, the possibility of simultaneously analyzing transfer functions and harmonics is investigated.

Transfer-Function Measurement with Sweeps

Reproduction of a sound field is a fundamental problem in acoustic signal processing. In this paper, we use a spherical harmonics analysis to derive performance bounds on how well an array of loudspeakers can recreate a three-dimensional (3-D) plane-wave sound field within a spherical region of space. Specifically, we develop a relationship between the number of loudspeakers, the size of the reproduction sphere, the frequency range, and the desired accuracy. We also provide analogous results for the special case of reproduction of a two-dimensional (2-D) sound field. Results are verified through computer simulations.

/pdf/reproduction-of-a-plane-wave-sound-field-using-an-array-of-a2b6tt8xjb.pdf

Reproduction of a plane-wave sound field using an array of loudspeakers

The acoustics in auditoria are determined by the properties of both the direct sound and the later arriving reflections. If electroacoustic means are used to repair disturbing deficiencies in the acoustics, one has to cope with unfavorable side effects such as localization problems and artificial impressions of the reverberant field (electronic flavor). To avoid those side effects, the concept of electroacoustic wave front synthesis is introduced. The underlying theory is based on the Kirchhoff–Helmholtz integral. In this new concept the wave fields of the sound sources on stage are measured by directive microphones; next they are electronically extrapolated away from the stage, and finally they are re‐emitted in the hall by one or more loudspeaker arrays. The proposed system aims at emitting wave fronts that are as close as possible to the real wave fields. Theoretically, there need not be any differences between the electronically generated wave fields and the real wave fields. By using the image source concept, reflections can be generated in the same way as direct sound.

Acoustic control by wave field synthesis

A new method is proposed to acquire impulse responses in concert halls with large signal‐to‐noise ratios and with a high resolution. In our proposal an omnidirectional loudspeaker is used which is driven by an amplified sweep: a signal containing all frequencies of interest smeared out in time. By using a deconvolution technique, an almost perfect pulse is obtained with a high peak pressure and a short effective duration. Measurements were made in two different concert halls to illustrate the practical implications of the new technique.

A new method to acquire impulse responses in concert halls

A method is proposed to calculate and measure impulse responses in an enclosure along closely spaced receiver arrays. Hence, instead of using a sparse distribution of receiver positions with single microphones, as is common practice now, arrays of microphones are applied to register the complex sound fields within enclosures. This way, there is a strong spatial correlation between adjacent responses, enabling one to analyze individual reflected wavefronts. It is shown that visualization of the recorded data in a two-dimensional domain, defined by detector position and travel time, gives a significantly improved insight in the structure of complex sound fields. This insight is further increased by applying the linear Radon transform (plane wave decomposition), yielding a representation of the data in the so-called ray parameter versus intercept time domain.

Array technology for acoustic wave field analysis in enclosures

In practice, impulse responses in enclosed spaces are calculated with algorithms that are based on the ray tracing model, the mirror image source model, or a mixture of both. Using those algorithms, however, the wave character of sound propagation is not properly taken into account and complex boundaries cannot be included. This paper presents an alternative approach adopted from the seismic imaging field. The proposed model is based on the concept of wave field extrapolation. Absorption properties of the boundaries can be specified in detail by means of reflection matrices. Propagation between boundaries is formulated by propagation matrices. Impulse responses along an array of receivers are numerically simulated by executing a sequence of matrix multiplications that can be interpreted as generalized spatial convolutions. Diffraction phenomena due to the finiteness and irregularity of the boundaries are correctly taken into account. The proposed algorithm is illustrated on a two-dimensional configuration...

A wave field extrapolation approach to acoustical modeling in enclosed spaces

Sound propagation in enclosed spaces is characterized by reflections at the boundaries of the enclosure. Reflections can be wanted in the case when they support the direct sound or give a feeling of envelopment or they can be unwanted when they lead to echoes and colouration. When measuring multiple impulse responses in an enclosed space along an array the reflections can be mapped to the reflecting objects. Similar to seismic exploration, medical diagnostics, and underwater acoustics, an image of the reflecting objects is obtained in terms of reflected energy. The imaging process is based on inverse wave field extrapolation with the Kirchhoff–Helmholtz and Rayleigh integrals. The inverse of the imaging process recreates the measured impulse responses from the image and it allows one to remove or alter reflecting objects in the image and investigate their influence on the wave field in the enclosed space in a physically correct way. This can be verified by reimaging the altered wave field. Preliminary res...

D. de Vries

Papers

Acoustic control by wave field synthesis

A new method to acquire impulse responses in concert halls

Array technology for acoustic wave field analysis in enclosures

A wave field extrapolation approach to acoustical modeling in enclosed spaces

Acoustic imaging in enclosed spaces: Analysis of room geometry modifications on the impulse response