Sampling theorems associated with offset linear canonical transform by polar coordinates

TL;DR

This paper develops sampling theorems for the offset linear canonical transform and related Hankel transform in polar coordinates, enabling efficient interpolation of bandlimited signals in these domains.

Contribution

It introduces two new sampling theorems for bandlimited functions in OLCT and OLCHT domains, improving computational efficiency and applicability.

Findings

Derived sampling theorems based on Stark's interpolation formulas

First formula is concise and broadly applicable

Second formula offers better computational efficiency

Abstract

The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important signal analysis tool in many fields of signal processing and medical imaging. This study investigates two sampling theorems for interpolating bandlimited and highest frequency bandlimited functions in the OLCT and offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark's interpolation formulas, we derive the sampling theorems for bandlimited functions in the OLCT and OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity.