Fourier-Bessel representation for signal processing: A review

Abstract

Several applications, analysis and visualization of signal demand representation of time-domain signal in different domains like frequency-domain representation based on Fourier transform (FT). Representing a signal in frequency-domain, where parameters of interest are more compact than in original form (time-domain). It is considered that the basis functions which are used to represent the signal should be highly correlated with the signal which is under analysis. Bessel functions are one of the set of basis functions which have been used in literature for representing non-stationary signals due to their damping (non-stationary) nature, and the representation methods based on these basis functions are named as Fourier-Bessel series expansion (FBSE) and Fourier-Bessel transform (FBT). The main purpose of this paper is to present a review related to theory and applications of FBSE and FBT methods. Roots calculation of Bessel functions, the relation between root order of Bessel function and frequency, advantages of Fourier-Bessel representation over FT have also been included in the paper. In order to make the implementation of FBSE based decomposition methods easy, the pseudo-code of decomposition methods are included. The paper also describes various applications of FBSE and FBT based methods present in the literature. Finally, the future scope of the Fourier-Bessel representation is discussed. © 2023 Elsevier Inc.