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

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 2π, 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.

Sampling theorems in the OLCT and the OLCHT domains by polar coordinates

“…In a recent work [33], we introduced the knowledge related to the 2D OLCT and the OLCHT in polar coordinates. In order to facilitate a indepth study of the integral transformation of the OLCT, we give some mathematical definitions in polar coordinates.…”

“…Compared with Theorem 1 of [33], it is more adaptable and concise. This is also a direct extension of the results in [33].…”

“…Based on our previous work [33], the purpose of this paper is to study two kinds of sampling theorems for Ω bandlimited f (r, θ) and highest frequency ω p = K 2π bandlimited functions from samples at the normalized zeros α nj in radius and at the uniformly spaced points 2πl 2K+1 in azimuuth in the OLCT and the OLCHT domains in polar coordinates. The results of the study show that due to the consistency of the order of the OLCHT, the interpolation formula in the OLCHT domain is superior to the interpolation formula in the OLCT domain in terms of computational complexity.…”