Quantum Fourier transform (QFT) transformation plays a very important role in the design of many quantum algorithms. Fractional (FRFT), as an extension transform, is particularly due to its algorithm. In this paper, new reformulation weighted fractional (WFRFT) proposed order realize FRFT; however, we found that can be applied other transformations, and therefore, paper presents Hartley (WFRHT)...

An efficient method for implementing closed form discrete fractional Fourier transform for the purpose of signal compression is presented. Implementation method is compared with that of existing closed form discrete fractional Fourier transform, with respect to computational complexity, variance of quantization error, signal to noise ratio and number of bits for the representation of coefficien...

Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics configuration for performing the fractional-Fourier-transform operation [J. Opt. Soc. Am. A 10, 2181 (1993)] provides a scaled output using a fixed lens. For obtaining a non-scaled...

Traditional Fast Fourier Transform algorithm makes the implementation of the multicarrier system feasible and attractive with respect to single-carrier systems. However, when the channel is doubly selective (i.e. time-frequencyselective), this traditional methodology fails. Since the channel frequency response is rapidly time-varying as a result the optimal transmission/reception methodology no...

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asympto...

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally...

As the one-dimensional (1-D) Fourier transform can be extended into the 1-D fractional Fourier transform (FRFT), we can also generalize the two-dimensional (2-D) Fourier transform. Sahin et al. have generalized the 2-D Fourier transform into the 2-D separable FRFT (which replaces each variable 1-D Fourier transform by the 1-D FRFT, respectively) and 2D separable canonical transform (further rep...

The paper deals with fractional derivative introduced by means of Fourier transform. The explicit form of the kernel of general derivative operator acting on the functions analytic on a curve in complex plane is deduced and the correspondence with some well known approaches is shown. In particular it is shown how the uniqueness of the operation depends on the derivative order type (integer, rat...