A new signal-adaptive joint time-frequency distribution for the analysis of nonstationary signals is proposed. It is based on a fractionalFourier-domain realization of the weighted Wigner distribution producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms. Improvement over the standard time-frequency representations is achieved when the principal ...

We present much briefer and more direct and transparent derivations of some sampling and series expansion relations for fractional Fourier and other transforms. In addition to the fractional Fourier transform, the method can also be applied to the Fresnel, Hartley, and scale transform and other relatives of the Fourier transform. ? 2003 Published by Elsevier B.V.

The approximate solutions of the time fractional advection-dispersion equation are presented in this article. nonlocal nature solute movement and nonuniformity fluid flow velocity process lead to formation a heterogeneous system, which can be modeled using equation, generalizes classical replaces derivative with Caputo derivative. Researchers use variety numerical techniques study such models, ...

We begin with an introduction to a calculus of fractional finite differences. We extend the discrete Laplace transform to develop a discrete transform method. We define a family of finite fractional difference equations and employ the transform method to obtain solutions. AMS subject classification: 39A12, 26A33.

Previous generalizations of the fractional Fourier transform to two dimensions assumed separable kernels. We present a nonseparable definition for the two-dimensional fractional Fourier transform that includes the separable definition as a special case. Its digital and optical implementations are presented. The usefulness of the nonseparable transform is justified with an image-restoration exam...

The fractional Fourier transform is more general and exible than the ordinary Fourier transform, but its optical and digital implementation is just as e cient. This underlies its potential for generalizations and improvements in every area of digital and optical signal processing. Here we consider applications of the transform to ltering, estimation and restoration. We see that the use of fract...

In this paper, Wavelet Transform, Fractional Fourier Transform (FrFT) and Fractional Cosine Transform (FrCT) are compared using Mean Square Error (MSE) and Peak signal-toNoise Ratio (PSNR) in the field of image compression. Wavelet provides better MSE and PSNR at lower Compression Ratio (CR), whereas FrFT provides good result at higher CR and FrCT provides same results as that of Wavelet at hig...

Abstract: This paper aims to apply the Laplace transform for solving linear fractional-order differential equation. The Laplace transform is a powerful tool in applied mathematics and engineering. It will allow us to transform fractional differential equations into algebraic equations and then by solving this algebraic equations, we can obtain the unknown function by using the Inverse Laplace T...

The present study introduces a new technique of homotopy perturbation method for the solution of systems of fractional partial differential equations. The proposed scheme is based on Laplace transform and new homotopy perturbation methods. The fractional derivatives are considered in Caputo sense. To illustrate the ability and reliability of the method some examples are provided. The results ob...

Watermark schemes content-based provide one way to solve the veracity and integrity of speech content. Some existed content-based schemes are vulnerable to feature-analysed substitution attack. Aiming to solve the problems, a secure speech content authentication algorithm is proposed, on the basic of the undeterminate angle of discrete fractional fourier transform. In the paper, the definition ...