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...

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...

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...

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...

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...

A mathematical theory on the computational complexity of the Discrete Fourier Transform (DFT) is required, independently of any kind of known Fast Fourier Transform (FFT) algorithm.

This paper is part 4 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). We demonstrate an approach to mitigating spectral leakage based on windowing...