Mathematical Background

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


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.


Unit Sphere Spherical Harmonic Dirac Delta Function Legendre Function Spherical Harmonic Coefficient 
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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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