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Acoustical Background

  • Boaz RafaelyEmail author
Chapter
  • 1.4k Downloads
Part of the Springer Topics in Signal Processing book series (STSP, volume 8)

Abstract

The mathematical background for functions defined on the unit sphere was presented in Chap.  1. Spherical harmonics played an important role in presenting and manipulating these functions. In this chapter, functions on the sphere are defined through the formulations of fields in three dimensions. Although sound fields are of primary concern in this book, which is oriented towards microphone arrays, the material presented here can be applied to scalar fields in general. This chapter begins by presenting the acoustic wave equation in Cartesian and spherical coordinates , with possible solutions. Solutions to the wave equation in spherical coordinates are shown to involve spherical harmonics and spherical Bessel and Hankel functions . Having formulated the fundamental solutions, sound fields due to a plane wave and a point source are presented, including an analysis of the effect of a rigid sphere introduced into the sound field. The latter is useful for describing the sound field around a microphone array configured over a rigid sphere, for example. The chapter concludes with a formulation of the three-dimensional translation of sound fields.

Keywords

Spherical Harmonic Sound Pressure Sound Field Rigid Sphere Microphone Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringBen-Gurion University of the NegevBeer-shevaIsrael

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