Mathematical background

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

This chapter provides the mathematical background necessary for studying spherical array processing. Spherical arrays typically sample functions on a sphere (e.g. sound pressure); therefore, this chapter begins by presenting the spherical coordinate system, as well as some examples of functions on the sphere. Spherical harmonics are a central theme of this book as they form a basis for representing functions on the sphere. Therefore, spherical harmonics are first defined and illustrated, and then an introduction to the spherical Fourier transform and a description of functions on the sphere in Hilbert space follows. The chapter concludes with a presentation of the topics of rotation, convolution, and correlation defined for functions on the sphere.

Original languageEnglish
Title of host publicationSpringer Topics in Signal Processing
PublisherSpringer Science and Business Media B.V.
Pages1-31
Number of pages31
DOIs
StatePublished - 1 Jan 2019

Publication series

NameSpringer Topics in Signal Processing
Volume16
ISSN (Print)1866-2609
ISSN (Electronic)1866-2617

Keywords

  • Balloon Plot
  • Cartesian coordinatesCartesian Coordinates
  • Spherical Fourier Transform
  • Spherical Harmonic Domain
  • rotationRotation

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