The spherical linear canonical transform: Definition and properties

Hui Zhao; Bing Zhao Li

doi:10.1016/j.ijleo.2023.170906

The spherical linear canonical transform: Definition and properties

Hui Zhao, Bing Zhao Li^*

^*Corresponding author for this work

School of Mathematics and Statistics

Beijing Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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.

Original language	English
Article number	170906
Journal	Optik
Volume	283
DOIs	https://doi.org/10.1016/j.ijleo.2023.170906
Publication status	Published - Jul 2023

Keywords

Convolution theorems
Spherical Fourier transform
Spherical linear canonical Hankel transform
Spherical linear canonical transform
Spherical polar coordinates

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10.1016/j.ijleo.2023.170906

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title = "The spherical linear canonical transform: Definition and properties",

abstract = "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.",

keywords = "Convolution theorems, Spherical Fourier transform, Spherical linear canonical Hankel transform, Spherical linear canonical transform, Spherical polar coordinates",

author = "Hui Zhao and Li, {Bing Zhao}",

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year = "2023",

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doi = "10.1016/j.ijleo.2023.170906",

language = "English",

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AU - Li, Bing Zhao

PY - 2023/7

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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

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DO - 10.1016/j.ijleo.2023.170906

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SN - 0030-4026

VL - 283

JO - Optik

JF - Optik

M1 - 170906

ER -

The spherical linear canonical transform: Definition and properties

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Keywords

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