TY - JOUR

T1 - The spherical linear canonical transform

T2 - Definition and properties

AU - Zhao, Hui

AU - Li, Bing Zhao

N1 - Publisher Copyright:
© 2023 Elsevier GmbH

PY - 2023/7

Y1 - 2023/7

N2 - The spherical Fourier transform has attracted considerable attention in the fields of acoustics, optics, and heat because of its superiority in solving practical problems- within the confines of spherical symmetry. A spherical linear canonical transform in spherical polar coordinates is investigated in this study. First, definitions of the spherical linear canonical transform and spherical linear canonical Hankel transform are proposed. Second, the relationship between the spherical linear canonical transform and spherical linear canonical Hankel transform is derived based on the orthogonality of the spherical harmonics. Finally, several essential properties of the proposed spherical linear canonical transform were obtained based on this relationship, including linearity, inversion formulas, shifts, and convolution theorems. Finally, potential applications of the spherical linear canonical transform are discussed.

AB - The spherical Fourier transform has attracted considerable attention in the fields of acoustics, optics, and heat because of its superiority in solving practical problems- within the confines of spherical symmetry. A spherical linear canonical transform in spherical polar coordinates is investigated in this study. First, definitions of the spherical linear canonical transform and spherical linear canonical Hankel transform are proposed. Second, the relationship between the spherical linear canonical transform and spherical linear canonical Hankel transform is derived based on the orthogonality of the spherical harmonics. Finally, several essential properties of the proposed spherical linear canonical transform were obtained based on this relationship, including linearity, inversion formulas, shifts, and convolution theorems. Finally, potential applications of the spherical linear canonical transform are discussed.

KW - Convolution theorems

KW - Spherical Fourier transform

KW - Spherical linear canonical Hankel transform

KW - Spherical linear canonical transform

KW - Spherical polar coordinates

UR - http://www.scopus.com/inward/record.url?scp=85162247941&partnerID=8YFLogxK

U2 - 10.1016/j.ijleo.2023.170906

DO - 10.1016/j.ijleo.2023.170906

M3 - Article

AN - SCOPUS:85162247941

SN - 0030-4026

VL - 283

JO - Optik

JF - Optik

M1 - 170906

ER -