Abstract.In this paper, the generalized Bessel matrix polynomials are introduced, starting from the hypergeometric matrix function. Integral form, Rodrigues’s formula and generating matrix function are then developed for the generalized Bessel matrix polynomials. These polynomials appear as finite series solutions of second-order matrix differential equations and orthogonality property for the ...

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

AA-LP Anti-aliasing lowpass AC3 Adaptive transform coder 3 ACR Absolute-category rating ADC Analog-to-digital converter ADPCM Adaptive differential pulse-code modulation AEC Acoustic echo cancellation / caneller AIR Acoustic impulse response ALP Adaptive lattice predictor ANC Active noise control or adaptive noise canceller AP Affine projection APC Adaptive predictive coding AR Auto-regressive ...

A Fourier-Bessel equivalent of the plane wave technique is employed to theoretically analyze a circular photonic crystal structure containing both radial and rotational periodicity. The presence of the 12-fold rotational symmetry in the dielectric profile results in a 12-times reduction in the order of the matrix diagonalized when cast using the Fourier-Bessel basis functions. In addition, the ...

Radial sampling of the NMR time domain has recently been introduced to speed up data collection significantly. Here, we show that radially sampled data can be processed directly using Fourier transforms in polar coordinates. We present a comprehensive theoretical analysis of the discrete polar Fourier transform, and derive the consequences of its application to radially sampled data using linea...

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 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...

An improved almost everywhere lower bound is given for Hausdorff dimension under vertical projections in the first Heisenberg group, with respect to Carnot-Carathéodory metric. This improves known bound, and answers a question of Fässler Hovila. The approach uses Euclidean Fourier transform, Basset's integral formula, modified Bessel functions second kind.

The linear canonical transform (LCT) is the name of a parameterized continuum of transforms that include, as particular cases, many widely used transforms in optics such as the Fourier transform, fractional Fourier transform, and Fresnel transform. It provides a generalized mathematical tool for representing the response of any first-order optical system in a simple and insightful way. In this ...

Majority of the hodograph transform solutions of the one-dimensional nonlinear shallow-water wave equations are obtained through integral transform techniques. This approach, however, might involve evaluation of elliptic integrals, which are highly singular. Here, we couple the hodograph transform approach with the classical eigenfunction expansion method rather than integral transform techniqu...