Fractional Fourier Transform, which is a generalization of the classical Fourier Transform, is a powerful tool for the analysis of transient signals. The discrete Fractional Fourier Transform Hamiltonians have been proposed in the past with varying degrees of correlation between their eigenvectors and Hermite Gaussian functions. In this paper, we propose a new Hamiltonian for the discrete Fract...

here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...

nowadays, radar systems have many applications and radar imaging is one of the most important of these applications. inverse synthetic aperture radar (isar) is used to form an image from moving targets. conventional methods use fourier transform to retrieve doppler information. however, because of maneuvering of the target, the doppler spectrum becomes time-varying and the image is blurred. joi...

In the next two lectures, we will continue to expand our toolbox for computing in frequency domain, by adding two important computational tools. The first, the Fast Fourier Transform (FFT) is a family of algorithms for efficiently computing the Discrete Fourier Transform. These algorithms are of great practical importance, as theymake it possible to perform frequency domain analysis of very lar...

It is shown that number theoretic transforms (NTT) can be used to compute discrete Fourier transform (DFT) very efficiently. By noting some simple properties of number theory and the DFT, the total number of real multiplications for a length-P DFT is reduced to (P — 1). This requires less than one real multiplication per point. For a proper choice of transform length and NTT, the number of shif...

  In this article, vibration analysis of an Euler-Bernoulli beam resting on a Pasternak-type foundation is studied. The governing equation is solved by using a spectral finite element model (SFEM). The solution involves calculating wave and time responses of the beam. The Fast Fourier Transform function is used for temporal discretization of the governing partial differential equation into a se...

the present study is the first to analyze the dynamic response of a poroelastic beam subjected to a moving force. moreover, the influences of attached mass-spring systems and non-ideal supports (with local movements in the supporting points or base due to the presence of factors such as gaps, unbalanced masses, and friction or seismic excitations) on the responses were investigated. non-ideal s...

The cubic Klein-Gordon equation is a simple but non-trivial partial differential equation whose numerical solution has the main building blocks required for the solution of many other partial differential equations. In this study, the library 2DECOMP&FFT is used in a Fourier spectral scheme to solve the Klein-Gordon equation and strong scaling of the code is examined on thirteen different machi...

1 Fourier Transform 1 1.1 Properties of the Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Schwartz space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Convergence in S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Fourier Transform in L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Fouri...