Two Bessel sequences are orthogonal if the composition of the synthesis operator of one sequence with the analysis operator of the other sequence is the 0 operator. We characterize when two Bessel sequences are orthogonal when the Bessel sequences have the form of translates of a finite number of functions in L(R). The characterizations are applied to Bessel sequences which have an affine struc...

A polynomial approximation to Bessel functions that arises from an electromagnetic scattering problem is examined. The approximation is extended to Bessel functions of any integer order, and the relationship to the Taylor series is derived. Numerical calculations show that the polynomial approximation and the Taylor series truncated to the same order have similar accuracies.

We present a new computation scheme for the integral expressions describing the contributions of single aberrations to the diffraction integral in the context of an extended Nijboer-Zernike approach. Such a scheme, in the form of a power series involving the defocus parameter with coefficients given explicitly in terms of Bessel functions and binomial coefficients, was presented recently by the...

This paper reports a new procedure for specifying monochromatic nonradiating ~NR! current distributions ~NR sources! and the electric and magnetic fields they produce ~NR fields!. Vector spherical harmonics and a Fourier–Bessel series are used to derive a new vector spherical-wave expansion for continuous NR fields confined within a spherical volume. The analysis yields complete orthogonal sets...

We review the Fourier-Laguerre transform, an alternative harmonic analysis on the three-dimensional ball to the usual Fourier-Bessel transform. The Fourier-Laguerre transform exhibits an exact quadrature rule and thus leads to a sampling theorem on the ball. We study the definition of convolution on the ball in this context, showing explicitly how translation on the radial line may be viewed as...

The wide-sense stationary-uncorrelated scattering (WSSUS) channel model is a commonly employed model for the multipath channel experienced in mobile communications. The second-order statistics of these channels are described by the delay cross-power density h( ; t) or by its t-Fourier transform, the scattering function Sh( ; ). This paper presents an analysis of the delay cross-power density an...

In this paper some Turán type inequalities for the general Bessel function, monotonicity and bounds for its logarithmic derivative are derived. Moreover we find the series representation and the relative extrema of the Turánian of general Bessel functions. The key tools in the proofs are the recurrence relations together with some asymptotic relations for Bessel functions.

The purpose of this paper is to compare the efficacy of two algorithms used for denoising underwater acoustic signals affected by ambient noise. The two denoising techniques are, (i) Fourier Bessel (FB) expansion based denoising algorithm and (ii) Empirical Mode Decomposition (EMD)-Fourier Bessel (FB) based denoising algorithm. Sea water normally contains unwanted background noise called ambien...