This paper is concerned with the definitions of the discrete fractional Hartley transform (DFRHT) and the discrete fractional Fourier transform (DFRFT). First, the eigenvalues and eigenvectors of the discrete Fourier and Hartley transform matrices are investigated. Then, the results of the eigendecompositions of the transform matrices are used to define DFRHT and DFRFT. Also, an important relat...

The paper presents a new closed-form expression for the fractional Fourier transform of generalized Triangular and Welch window functions. Fractional Fourier Transform (FrFT) is a parameterized transform having an adjustable transform parameter which makes it more flexible and superior over ordinary Fourier transform in several applications. It is an important tool used in signal processing for...

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importanc...

In this paper an approximate analytical solution of the fractional Zakharov-Kuznetsov equations will be obtained with the help of the reduced differential transform method (RDTM). It is in-dicated that the solutions obtained by the RDTM are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

Analysis of Chirp Signal with Fractional Fourier Transform POOJA MOHINDRU*, RAJESH KHANNA1 and S S BHATIA2 Department of Electronics and Communication Engineering, University College of Engineering, Punjabi University, Patiala 147 004, Punjab, India 1Department of Electronics & Communication Engineering, Thapar University, Patiala 147 004, Punjab, India 2School of Mathematics, Thapar University...

In Baraka’s paper [2], he obtained the Littlewood-Paley characterization of Campanato spaces L and introduced Lp,λ,s spaces. He showed that L2,λ,s = (−△)− s 2L for 0 ≤ λ < n+ 2. In [7], by using the properties of fractional Carleson measures, J Xiao proved that for n ≥ 2, 0 < α < 1. (−△)−α2 L is essential the Qα(R) spaces which were introduced in [4]. Then we could conclude that Qα(R) = L2,n−2α...

A new method for the discrete fractional Fourier transform (DFRFT) computation is given in this paper. With the help of this method, the DFRFT of any angle can be computed by a weighted summation of the DFRFTs with the special angles.

This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained. Then, the relationship is extended to a general set of nonuniform samples of band-limited signal associated with the fractional Fourier transform. Finally, the two dimensional case is investigate...

The continuous fractional Fourier transform (FRFT) performs a spectrum rotation of signal in the time–frequency plane, and it becomes an important tool for time-varying signal analysis. A discrete fractional Fourier transform has been recently developed by Santhanam and McClellan, but its results do not match those of the corresponding continuous fractional Fourier transforms. In this paper, we...

We compare the Riemann–Liouville fractional integral (fI) of a function f(z) with the Liouville fI of the same function and show that there are cases in which the asymptotic expansion of the former is obtained from those of the latter and the difference of the two fIs. When this happens, this fact occurs also for the fractional derivative (fD). This method is applied to the derivation of the as...