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Fourier Acoustics: Sound Radiation and Nearfield Acoustical Holography

TL;DR: The Inverse Problem: Cylindrical NAH. as discussed by the authors The Inverse problem: Planar NAH and the Inverse NP-hardness of planar plane waves.
Abstract: Preface. Fourier Transforms & Special Functions. Plane Waves. The Inverse Problem: Planar NAH. Cylindrical Waves. The Inverse Problem: Cylindrical NAH. Spherical Waves. Spherical NAH. Green Functions & the Helmholtz Integral. Index.
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Journal ArticleDOI
TL;DR: Alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations.
Abstract: Spherical microphone arrays have been recently studied for sound-field recordings, beamforming, and sound-field analysis which use spherical harmonics in the design. Although the microphone arrays and the associated algorithms were presented, no comprehensive theoretical analysis of performance was provided. This work presents a spherical-harmonics-based design and analysis framework for spherical microphone arrays. In particular, alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations. The analysis framework can also provide a useful guide for the design and analysis of more general spherical microphone arrays which do not use spherical harmonics explicitly.

522 citations


Cites background or methods from "Fourier Acoustics: Sound Radiation ..."

  • ...The spherical Fourier transform [9], or spherical harmonics decomposition [10], employed in this paper is briefly revised in this section....

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  • ...Substituting (2) in (6), the condition for exact sampling as in (6) is satisfied if the following holds: (7) Equation (7) can be considered as a modified version of the orthogonality property of the spherical harmonics [10], [13]....

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Journal ArticleDOI
TL;DR: A spherical harmonics analysis is used 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.
Abstract: 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.

378 citations

Book ChapterDOI
15 Apr 2005
TL;DR: The finite-difference time-domain (FDTD) solution of the Maxwell's equations is a robust and popular computational technique in science and engineering for modeling electromagnetic wave interactions with complex material structures as mentioned in this paper.
Abstract: The finite-difference time-domain (FDTD ) solution of Maxwell's equations is a robust and popular computational technique in science and engineering for modeling electromagnetic wave interactions with complex material structures. This article reviews key elements of the foundation of FDTD analysis as well as selected recent and emerging FDTD application areas. Keywords: finite-difference time domain; FDTD, Maxwell's equations; numerical methods; computations; electromagnetic waves; computational electrodynamics

294 citations

Journal Article
TL;DR: In this article, a unified theoretical framework covering arbitrarily shaped loudspeaker arrays for two and three-dimensional wave field synthesis has been presented, which is based on the concept of WFS.
Abstract: Wave field synthesis is a spatial sound field reproduction technique aiming at authentic reproduction of auditory scenes. Its theoretical foundation has been developed almost 20 years ago and has been improved considerably since then. Most of the original work on wave field synthesis is restricted to the reproduction in a planar listening area using linear loudspeaker arrays. Extensions like arbitrarily shaped distributions of secondary sources and three-dimensional reproduction in a listening volume have not been discussed in a unified framework so far. This paper revisits the theory of wave field synthesis and presents a unified theoretical framework covering arbitrarily shaped loudspeaker arrays for twoand three-dimensional reproduction. The paper additionally gives an overview on the artifacts resulting in practical setups and briefly discusses some extensions to the traditional concepts of WFS.

276 citations


Cites methods from "Fourier Acoustics: Sound Radiation ..."

  • ...The three-dimensional free-field Green’s function is given as [25]...

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  • ...The solution of the homogeneous wave equation for a bounded region V with respect to inhomogeneous boundary conditions is given by the KirchhoffHelmholtz integral [25]...

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  • ...According to [25] two different techniques exist to derive monopole only versions of the Kirchhoff-Helmholtz integral: the simple source approach and a modification of the free-field Green’s function used in the KirchhoffHelmholtz integral....

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  • ...A suitable Neumann Green’s function for a planar/linear boundary ∂V is given by [25]...

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  • ...The two-dimensional free-field Green’s function is given as [25]...

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Proceedings ArticleDOI
13 May 2002
TL;DR: Spherical harmonics analysis is used to establish theory and design of a higher order recording system, which comprises an array of small microphones arranged in a spherical configuration and associated signal processing, which has implications to the advancement of future sound field reconstruction systems.
Abstract: A major problem in sound field reconstruction systems is how to record the higher order (> 1) harmonic components of a given sound field. Spherical harmonics analysis is used to establish theory and design of a higher order recording system, which comprises an array of small microphones arranged in a spherical configuration and associated signal processing. This result has implications to the advancement of future sound field reconstruction systems. An example of a third order system for operation over a 10∶1 frequency range of 340 Hz to 3.4 kHz is given.

252 citations