The two-dimensional OLCT of angularly periodic functions in polar coordinates

TL;DR

This paper extends the 2D offset linear canonical transform (OLCT) to polar coordinates, deriving related transforms and theorems that enhance understanding of angularly periodic functions in optics and signal processing.

Contribution

It introduces the 2D OLCT in polar coordinates, derives the OLCHT, and establishes shift and convolution theorems based on angular periodic functions.

Findings

Derived the OLCHT from the 2D OLCT in polar coordinates.

Established the relationship between 2D OLCT and OLCHT for periodic functions.

Proposed spatial shift and convolution theorems for 2D OLCT.

Abstract

The two-dimensional (2D) offset linear canonical transform (OLCT) in polar coordinates plays an important role in many fields of optics and signal processing. This paper studies the 2D OLCT in polar coordinates. Firstly, we extend the 2D OLCT to the polar coordinate system, and obtain the offset linear canonical Hankel transform (OLCHT) formula. Secondly, through the angular periodic function with a period of 2{\pi}, the relationship between the 2D OLCT and the OLCHT is revealed. Finally, the spatial shift and convolution theorems for the 2D OLCT are proposed by using this relationship.