Results 331 to 340 of about 744,050 (371)

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 ...
Liren Liu, Jianwen Hua, Guoqiang Li
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Fractional Fourier Transform: A Review

IETE Journal of Education, 2007
The fractional Fourier transform (FRFT) is the generalization of the classical Fourier transform (FT). The FRFT was introduced about seven decades ago as literature reveals.
Rajiv Saxena, Kulbir Singh
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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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The Fractional Fourier Transform and Applications

SIAM Review, 1991
This paper describes the “fractional Fourier transform,” which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the discrete Fourier transform (DFT) is based on integral roots of unity $e^{{{ - 2\pi i} / n}} $, the fractional Fourier transform is based on fractional roots of unity $e^{
David H. Bailey, Paul N. Swarztrauber
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Fractional Fourier transform reflectometry

SPIE Proceedings, 2014
In some OFDR implementations it is advantageous to use sinusoidal frequency tuning and to work in the linear range of the sinusoid. For a given scan frequency this limits the maximum length of the interrogated fiber. We propose a new method which allows exceedingly large delays while maintaining high scan rates.
Avishay Eyal, Lihi Shiloh
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Fractional Fourier transforms and imaging

Journal of the Optical Society of America A, 1994
The characteristics and properties of fractional Fourier transforms of an arbitrary degree, as implemented by a lens system, are presented. We describe the perfect imaging process and implement it by cascading a set of appropriate fractional-Fourier-transform elementary units of integer and/or fractional degree, forming generalized afocal systems.
Luís M. Bernardo, Olivério D. D. Soares   +1 more
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Quantum Fractional Fourier Transform

Frontiers in Optics / Laser Science, 2018
Fourier transform has taken place in different areas and applications, in this paper has been revised an important new form of application in the paradigm of quantum computing. Quantum Fourier transforms have gained increased attention with the rise of quantum walks, boson sampling, and quantum metrology [2]. In the Shor’s Algorithm it is used for find
Yesid Madrid, Martha Molina, Rafael Torres   +2 more
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Generalized fractional Fourier transforms

Journal of Physics A: Mathematical and General, 1997
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 and k = 4,
Yan Zhang, Jingde Zhang, Jiuxing Jiang, Shutian Liu   +3 more
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Beam analysis by fractional Fourier transform

Optics Letters, 2001
A method of spatial modal decomposition for optical beams by fractional Fourier transform, and its practical implementation with reduced complexity by use of modal interleavers, are discussed.
Haiqing Wei, Andrew G. Kirk, Xin Xue
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Fractional fourier transform: photonic implementation

Applied Optics, 1994
The family of fractional Fourier transforms permits presentation of a temporal signal not only as a function of time or as a pure frequency function but also as a mixed time and frequency function with a continuous degree of emphasis on time or on frequency features.
Adolf W. Lohmann, David Mendlovic
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