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Implementation of quantum and classical discrete fractional Fourier transforms [PDF]
Nature Communications, 2016 Fourier analysis has become a standard tool in contemporary science. Here, Weimann et al. report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform, with potential ...
Steffen Weimann +11 more
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Simplified fractional Fourier transforms [PDF]
Journal of the Optical Society of America A: Optics and Image Science, and Vision, 2000 The fractional Fourier transform (FRFT) has been used for many years, and it is useful in many applications. Most applications of the FRFT are based on the design of fractional filters (such as removal of chirp noise and the fractional Hilbert transform) or on fractional correlation (such as scaled space-variant pattern recognition).
Soo-Chang Pei, Jian-Jiun Ding
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On fractional Fourier transform moments [PDF]
IEEE Signal Processing Letters, 2000 Based on the relation between the ambiguity function represented in a quasi-polar coordinate system and the fractional power spectra, the fractional Fourier transform moments are introduced. Important equalities for the global second-order fractional Fourier transform moments are derived and their applications for signal analysis are discussed.
Tatiana Alieva, Martin J. Bastiaans
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Unsteady two dimensional flow of non-newtönian fractional Casson fluid for an edge with heated boundaries [PDF]
Scientific ReportsThis study explores the transient flow and thermal behavior of incompressible non-Newtonian fluids, with a particular emphasis on Casson and fractional Casson models, which are widely applied in blood flow, lubricants, and polymer processing.
Sohail Nadeem +4 more
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The fractional fourier transform [PDF]
2001 European Control Conference (ECC), 2001 A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are discussed. An overview of applications which have so far received interest are given and some potential application areas remaining
Haldun M. Özaktas, M. Alper Kutay
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Fractional Fourier transforms of vortex Hermite-cosh-Gaussian beams
Results in Optics, 2021 In this paper, we investigate the propagation properties of a vortex Hermite-cosh-Gaussian beam (vHChGB) passing through a fractional Fourier transform (FRFT) optical system.
E.M. El Halba, Z. Hricha, A. Belafhal
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On the Fractional Derivative Duality in Some Transforms
Mathematics, 2023 Duality is one of the most interesting properties of the Laplace and Fourier transforms associated with the integer-order derivative. Here, we will generalize it for fractional derivatives and extend the results to the Mellin, Z and discrete-time Fourier
Manuel Duarte Ortigueira +1 more
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The Fractional Clifford-Fourier Transform [PDF]
Complex Analysis and Operator Theory, 2012 17 pages, accepted for publication in Complex Anal.
De Bie, Hendrik, De Schepper, Nele
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The discrete fractional Fourier transform [PDF]
IEEE Transactions on Signal Processing, 1999 Summary: We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform.
Cagatay Candan +2 more
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The generalized fractional fourier transform [PDF]
2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2012 A new transform, called the generalized fractional Fourier transform (gFrFT), is proposed. Originally, the eigenfunctions of the fractional Fourier transform (FrFT) are known as the Hermite Gaussian functions (HGFs). Besides, in optics, the HGFs are generalized to be the generalized Hermite Gaussian functions (gHGFs) and their adjoint functions (AgHGFs)
Soo-Chang Pei +2 more
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