TY - CHAP
T1 - Mathematical background
AU - Rafaely, Boaz
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Balloon Plot
KW - Cartesian coordinatesCartesian Coordinates
KW - Spherical Fourier Transform
KW - Spherical Harmonic Domain
KW - rotationRotation
UR - https://www.scopus.com/pages/publications/85101088409
U2 - 10.1007/978-3-319-99561-8_1
DO - 10.1007/978-3-319-99561-8_1
M3 - Chapter
AN - SCOPUS:85101088409
T3 - Springer Topics in Signal Processing
SP - 1
EP - 31
BT - Springer Topics in Signal Processing
PB - Springer Science and Business Media B.V.
ER -