We study the dynamics of accelerating Bessel beams and their corresponding apodized version. Presenting a closed analytical form for the intensity profile, we investigate the contribution of evanescent fields during the evolution for both cases. OCIS codes: (050.1960) Diffraction theory; (070.7345) Wave propagation Airy beams, as the first class of paraxial non-diffracting accelerating wave pac...

This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general solutions of differential operators. In particular, the harmonic Bessel RBF transforms were presented for high-dimensional data processing. It was also found ...

Various problems of Statistics, Mathematics, Radio Physics, Nuclear Atomic Fluid Mechanics, Engineering and Science can easily handle by applying integral transform techniques on their mathematical models. Problems heat equation, Schrodinger Laplace Helmholtz equation wave have solutions in terms Bessel functions. To solve such equations methods, we need to know the In this paper, authors discu...

We present a new method for time-frequency representation (TFR), which combines a Fourier Bessel (FB) series expansion and the Wigner-Ville distribution (WVD). The FB series decomposes a multi-component signal into a number of single component signals before the WVD is applied. and then WVD is applied on the single component signals to analyze its time-frequency distribution (TFD). The simulati...

In chirped pulse experiments, magnitude Fourier transform is used to generate frequency domain spectra. The application of window function as a tool for lineshape correction and signal-to-noise ratio (SnR) enhancement rarely discussed in spectroscopy, with the only exception using Kaiser-Bessel trivial rectangular window. We present specific function, called "Voigt-1D" window, designed spectros...

The Green function of Mumford-Shah functional in the absence of discontinuities is known to be a modified Bessel function of the second kind and zero degree. Such a Bessel function is regularized here and used as a filter for feature extraction. It is demonstrated in this paper that a Bessel filter does not follow the scale space smoothing property of bounded linear filters such as Gaussian fil...

Let the Bessel number of the second kind B(n, k) be the number of set partitions of [n] into k blocks of size one or two, and let the Bessel number of the first kind b(n, k) be the coefficient of x in −yn−1(−x) , where yn(x) is the nth Bessel polynomial. In this paper, we show that Bessel numbers satisfy two properties of Stirling numbers: The two kinds of Bessel numbers are related by inverse ...

This report addresses the problem of speech enhancement employing the Minimum Mean-Square Error (MMSE) of β-order Short Time Spectral Amplitude (STSA). We present an analytical solution for β-order MMSE estimator where Discrete Fourier Transform (DFT) coefficients of (clean) speech are modeled by Laplacian distributions. Using some approximations for the joint probability density function and t...