Trispectrum and higher order spectra for non-Gaussian homogenous and isotropic field on the 2D-plane

TL;DR

This paper explores the mathematical characterization of non-Gaussian isotropic fields on the plane using higher order spectra like the trispectrum, expressed through Bessel functions, with applications of Poisson formulae.

Contribution

It provides a detailed description of the trispectrum and higher order spectra for non-Gaussian isotropic fields using Bessel functions and Poisson formulae, advancing theoretical understanding.

Findings

Derivation of trispectrum and higher order spectra in terms of Bessel functions

Poisson formulae for spectrum and bispectrum are established

Analysis of specific Bessel function integrals related to the spectra

Abstract

In this paper we study the non-Gaussian homogenous and isotropic field on the plane in frequency domain. The trispectrum and higher order spectra of such a field are described in terms of Bessel functions. Poisson formulae are given for the spectrum and for the bispectrum. Some particular integrals of Bessel functions are considered as well.