Two-dimensional OLCT of angularly periodic functions in polar coordinates

被引：3

作者：

Zhao, Hui ^{[1
,2
]}

Li, Bing-Zhao ^{[1
,2
]}

机构：

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Beijing Inst Technol, Beijing Key Lab MCAACI, Beijing 100081, Peoples R China

来源：

DIGITAL SIGNAL PROCESSING | 2023年 / 134卷

基金：

中国国家自然科学基金;

关键词：

Polar coordinates; Offset linear canonical transform; Offset linear canonical Hankel transform; Spatial shift theorem; Convolution theorem; LINEAR CANONICAL TRANSFORM; FRACTIONAL FOURIER; EIGENFUNCTIONS; CONVOLUTION; DOMAIN;

D O I：

10.1016/j.dsp.2022.103905

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

Searching for novel signal processing theories and methods has always been a research hotspot in the field of modern signal processing. The existing transform methods for dealing with non-stationary signals are based on traditional Cartesian coordinates, which are very inconvenient to deal with signals naturally described by polar coordinates. This paper studies two-dimensional offset linear canonical transform (OLCT) in polar coordinates. Firstly, the definition of the two-dimensional OLCT in polar coordinates is proposed, and the offset linear canonical Hankel transform (OLCHT) formula is derived. Secondly, the relationship between the OLCT and the OLCHT is revealed through the angular periodic function. Then, some properties of the two-dimensional OLCT in polar coordinates are proved based on the mentioned relationship. Finally, the proposed two-dimensional OLCT is applied in the computed tomography. The effectiveness and feasibility of the proposed method are verified by simulation experiments.& COPY; 2022 Elsevier Inc. All rights reserved.

引用

页数：15

共 35 条

[1] THE FRACTIONAL FOURIER-TRANSFORM AND TIME-FREQUENCY REPRESENTATIONS [J].