A Note on the Convolution of Circle Impulses

TL;DR

This paper derives a formula for convolving two circle impulses using Bessel function addition theorems, providing a mathematical tool relevant for signal processing involving circular geometries.

Contribution

It introduces a novel convolution formula for circle impulses based on classical Bessel function addition theorems.

Findings

Derived an explicit convolution formula for circle impulses.

Utilized classical Bessel function addition theorems in the derivation.

Provides a mathematical foundation for circular signal processing applications.

Abstract

We present a formula for the convolution $\delta_{C_1}*\delta_{C_2}$ of two circle impulses. The derivation uses a classical addition theorem for Bessel functions.