Results 291 to 300 of about 42,784 (333)

Fractional Fourier–Jacobi type transform

ANNALI DELL'UNIVERSITA' DI FERRARA, 2020
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Coincidence subwavelength fractional Fourier transform

Journal of the Optical Society of America A, 2006
The coincidence subwavelength fractional Fourier transforms (FRTs) with entangled photon pairs and incoherent light radiation are introduced as an extension of the recently introduced coincidence FRT. Optical systems for implementing the coincidence subwavelength FRTs are designed.
Yangjian, Cai, Qiang, Lin, Shi-Yao, Zhu
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On Namias's Fractional Fourier Transforms

IMA Journal of Applied Mathematics, 1987
\textit{V. Namias} [J. Inst. Math. Appl. 25, 241-265 (1980; Zbl 0434.42014)] developed a theory of fractional powers for the Fourier transform and obtained a number of fractional formulae which he used to solve several types of Schrödinger equation. In this paper the authors attempt to provide the necessary mathematical framework for Namias' idea in ...
McBride, A. C., Kerr, F. H.
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The fractional Fourier–Jacobi wavelet transform

The Journal of Analysis, 2023
The main objective of this study is to define the fractional Jacobi translation and fractional Jacobi convolution, as well as to analyze the fractional Fourier-Jacobi wavelet transform and its fundamental properties. Additionally, an inversion formula and a Parseval relation for the continuous fractional Fourier-Jacobi wavelet transform are derived.
Othman Tyr, Faouaz Saadi
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Fractional Fourier transform

Proceedings of the International Conference on Advances in Computing, Communications and Informatics, 2012
The Fractional Fourier transform (FRFT), which provides generalization of conventional Fourier Transform was introduced many years ago in mathematics literature by Namias. In this paper, definition, properties of fractional Fourier transform and its relationship with other transforms is discussed.
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Fractional-Fourier-transform calculation through the fast-Fourier-transform algorithm

Applied Optics, 1996
A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1.
J, García, D, Mas, R G, Dorsch
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Fractional Fourier Transforms

2003
In the next few lectures we provide a brief overview of Fourier analysis and how it has been used to model lin- ear physical phenomena, particularly the reversible propagation of scalar waves in homogeneous media and the irreversible diffusion of one molecular species within another.
Bruce J. West, Mauro Bologna, Paolo Grigolini   +2 more
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Fractional Fourier–Kravchuk transform

Journal of the Optical Society of America A, 1997
We introduce a model of multimodal waveguides with a finite number of sensor points. This is a finite oscillator whose eigenstates are Kravchuk functions, which are orthonormal on a finite set of points and satisfy a physically important difference equation.
Natig M. Atakishiyev, Kurt Bernardo Wolf
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Extended fractional Fourier transforms

Journal of the Optical Society of America A, 1997
The concept of an extended fractional Fourier transform (FRT) is suggested. Previous FRT’s and complex FRT’s are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple ...
Jianwen Hua, Liren Liu, Guoqiang Li
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Generalized fractional Fourier transforms

Journal of Physics A: Mathematical and General, 1997
Summary: We generalize the definition of the fractional Fourier transform (FRT) by expanding the new definition proposed by Shih to the original definition. The generalized FRT is shown to have \(k\)-periodic eigenvalues with respect to the order of Hermite-Gaussian functions and will be reduced to the original FRT and Shih's FRT at the two limits with
Liu, Shutian, Jiang, Jiuxing, Zhang, Yan, Zhang, Jingde   +3 more
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