# Fourier-Bessel transform

## Fourier-Bessel transform

[‚fu̇r·ē‚ā ¦bes·əl ′tranz‚fȯrm]
(mathemtics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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From the Maxwell system (1)--(3) a differential equation for the azimuthal component of the electric field strength [E.sub.[phi]](p,[lambda],z) can be obtained, which after the integral Fourier-Bessel transform takes the form [8].
The Bessel functions form the orthogonal basis and decay over the time, so that the signals which do not overlap in both the time and the frequency domain, including single frequency signals and linear frequency modulated (LFM) signals, can be represented well using the Fourier-Bessel transform (FBT) or the Fourier-Bessel (FB) series expansion [15-18].
Venkataramaniah, "Fourier-Bessel transform and time-frequency-based approach for detecting manoeuvring air target in sea-clutter," IET Radar, Sonar and Navigation, vol.
Venkataramaniah, "Extracting micro-doppler radar signatures from rotating targets using fourier-bessel transform and time-frequency analysis," IEEE Transactions on Geoscience and Remote Sensing, vol.
The main aim of this paper is to establish an analog of Theorem 1.1 in the generalized Fourier-Bessel transform. We point out that similar results have been established in the Dunkl transform [3].
The generalized Fourier-Bessel transform we call the integral from [2]
Let f [member of] [L.sup.1.sub.[alpha],n], the inverse generalized Fourier-Bessel transform is given by the formula
The Fourier-Bessel transform of a function f [member of] D(R) is defined by
(i) The Fourier-Bessel transform [F.sub.[alpha]] is a topological isomorphism from D(R) onto H.
In isotropic case [??] depends only on the corresponding radial coordinate [rho] = [parallel][xi][parallel], and [[??].sub.1]([rho]) = [??]([xi]) is the Fourier-Bessel transform of [k.sub.1](r),
It is well known that the Fourier-Bessel transform of the exponential correlation function is
This leads to an estimation of the density [[??].sub.1] of the Bartlett-Spectrum using the 1-dimensional Fourier-Bessel transform as defined by Eq.

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