Mathematical properties of generalized Bessel functions and application to multi-tone sinusoidal frequency modulation

Abstract

The generalized Bessel function (GBF) is a multi-dimensional extension of the standard Bessel function. Two dimensional GBFs have been studied extensively in the literature and have found application in laser physics, crystallography, and electromagnetics. However, a more rigorous treatment of higher-dimensional GBFs is lacking. The GBF exhibits a rich array mathematical structure in regards to its partial differential equation representation, its asymptotic characterization, and its level sets. In this talk/paper, we explore these properties and connect spectral and ambiguity function optimization of a multi-tone SFM signal to finding the location of the roots of these generalized Bessel functions.