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.

/pdf/three-dimensional-surround-sound-systems-based-on-spherical-gts6rffrmw.pdf

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.

/pdf/binaural-cue-coding-part-ii-schemes-and-applications-39qaaj3pak.pdf

Binaural cue coding-Part II:Schemes and applications

The Sonification Handbook

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

Spherical microphone arrays have been recently studied for sound analysis and sound recordings, which have the advantage of spherical symmetry facilitating three-dimensional analysis. This paper complements the recent microphone array design studies by presenting a theoretical analysis of plane-wave decomposition given the sound pressure on a sphere. The analysis uses the spherical Fourier transform and the spherical convolution, where it is shown that the amplitudes of the incident plane waves can be calculated as a spherical convolution between the pressure on the sphere and another function which depends on frequency and the sphere radius. The spatial resolution of plane-wave decomposition given limited bandwidth in the spherical Fourier domain is formulated, and ways to improve the computation efficiency of plane-wave decomposition are introduced. The paper concludes with a simulation example of plane-wave decomposition.

/pdf/plane-wave-decomposition-of-the-sound-field-on-a-sphere-by-18uxxijpmr.pdf

Plane-wave decomposition of the sound field on a sphere by spherical convolution

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

The acoustics in auditoria is determined by the properties of both direct sound and reflections. If electroacoustic means are used to optimize the acoustics, one has to cope with unfavorable side effects such as localization problems and artificial impression of the reverberant field. To avoid those side effects, the concept of electroacoustic wave‐front synthesis is introduced. The underlying theory is based on the Huygens–Rayleigh integral. In this concept, the wave fields of the sound sources on stage are measured by directive microphones; next they are extrapolated by means of an electronic processor, and finally, they are re‐emitted in the hall by one or more loudspeaker arrays. Depending on the processor design, the wave‐front systems can be used for direct sound enhancement, for simulation of discrete early reflections, or for generation of reverberation. Application of the wave‐front synthesis concept also opens the door to a new approach of sound recording and reproduction.

Wave Front Synthesis: A New Direction in Electroacoustics

Use of Wave Field Synthesis for Natural Reinforced Sound

Experience with a Sound Enhancement System Based on Wavefront Synthesis

In an auditorium equipped with an electroacoutstic system the acoustic impulse response between source and receiver is the sum of the source receiver response of the auditorium boundaries and a contribution of the system. In the system contribution the source microphone response and the loudspeaker receiver response should be included. In the time domain this leads to a convolutional model to describe the acoustic performance of the system. Due to the convolutions the reflection density in the system response can become extremely high, which for reverberation enhancement systems leads to nonlinear decay curves

Peter Vogel

Papers

Acoustic control by wave field synthesis

Wave Front Synthesis: A New Direction in Electroacoustics

Use of Wave Field Synthesis for Natural Reinforced Sound

Experience with a Sound Enhancement System Based on Wavefront Synthesis

Electroacoustic system response in a hall: a convolution of impulse sequences