Various transforms are employed for signal processing to obtain useful information, which is not explicitly available when the signal is in the time domain. Most of the real time signals such as speech, biomedical signals, etc., are non-stationary signals. The Fourier transform (FT), used for most of the signal processing applications, determines the frequency components present in the signal b...

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily hig...

In this paper, the initial value problem is discussed for local fractional Caudrey-Dodd-Gibbon-Kaeada equation. The complex transform and new iterative method are used to solve problem, approximate analytical solutions obtained.

The main purpose of this paper is to present a new iterative transform method (NITM) and a modified fractional homotopy analysis transform method (MFHATM) for time-fractional Fornberg-Whitham equation. The numerical results show that the MFHATM and NITM are very efficient and highly accurate for nonlinear fractional differential equations. c ©2016 All rights reserved.

FRACTIONAL FOURIER INTEGRAL THEOREM AND FRACTIONAL FOURIER SINE AND COSINE TRANSFORM Saleem Iqbal, S.M. Raza, * LalaRukh Kamal and Farhana Sarwar Department of Mathematics/Physics, University of Balochistan, Quetta, Pakistan e-mail: fs1005,saleemiqbal81,[email protected]. ABSTRACT: The fractional Fourier transform (FRFT) is a generalization of the ordinary Fourier transform (FT). Recently...

The fractional wavelet transform (FRWT), which generalizes the classical wavelet transform, has been shown to be potentially useful for signal processing. Many fundamental results of this transform are already known, but the theory of multiresolution analysis and orthogonal wavelets is still missing. In this paper, we first develop multiresolution analysis associated with the FRWT and then deri...

In this paper, we develop some methods to save the bandwidth required in the fractional domain. The fractional domain is the transformed domain of the fractional Fourier transform (FRFT). It is the intermediate of the time domain and the frequency domain. We find that, with the aid of the fractional Hilbert transform and other techniques, we can save 112 or 314 of the bandwidth in the fractiona...

A numerical method for solving the fractional-order logistic differential equation with two different delays FOLE is considered. The fractional derivative is described in the Caputo sense. The proposed method is based upon Chebyshev approximations. The properties of Chebyshev polynomials are utilized to reduce FOLE to a system of algebraic equations. Special attention is given to study the conv...

The linear transform kernel for fractional Fourier transforms is derived. The spatial resolution and the space-bandwidth product for propagation in graded-index media are discussed in direct relation to fractional Fourier transforms, and numerical examples are presented. It is shown how fractional Fourier transforms can be made the basis of generalized spatial filtering systems: Several filters...

The performance of Orthogonal Frequency Division Multiple Access (OFDMA) system degrades significantly in doubly dispersive channels. This is due to the fact that exponential sub-carriers do not match the singular functions of this type of channels. To solve this problem, we develop a system whose sub-carriers are chirp functions. This is equivalent to exploiting Fractional Fourier Transform (F...