Fourier-Zernike Series of Convolutions on Disks

TL;DR

This paper explores the Fourier-Zernike series representation of convolutions on disks, providing a systematic analysis and examining the effects of zero-padding on the theory.

Contribution

It offers a comprehensive analytic framework for Fourier-Zernike series of convolutions on disks, including the impact of zero-padding.

Findings

Analytic expressions for Fourier-Zernike series of convolutions.

Insights into the effects of zero-padding on the series.

Systematic study of convolution properties on disk-supported functions.

Abstract

This paper presents a systematic study for analytic aspects of Fourier-Zernike series of convolutions of functions supported on disks. We then investigate different aspects of the presented theory in the cases of zero-padded functions.