Bispectrum for non-Gaussian homogenous and isotropic field on the plane

TL;DR

This paper characterizes the third order moments and bispectra of homogeneous isotropic fields on a plane, establishing a direct link between cumulants and bispectra using Bessel functions.

Contribution

It introduces a novel theoretical framework connecting third order cumulants and bispectra for isotropic fields on the plane.

Findings

Derived a one-to-one correspondence between cumulants and bispectra.

Expressed the relationship in terms of Bessel functions.

Provides a mathematical foundation for analyzing non-Gaussian isotropic fields.

Abstract

The object of this paper is to characterize the third order moments (cumulants) and bispectra of a homogeneous isotropic field defined on a plane. We establish a one to one correspondence between the third order cumulants and the bispectra of such a process in terms of Bessel functions.