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Fractional Fourier transforms in two dimensions

Journal of the Optical Society of America A, 2000
We analyze the fractionalization of the Fourier transform (FT), starting from the minimal premise that repeated application of the fractional Fourier transform (FrFT) a sufficient number of times should give back the FT. There is a qualitative increase in the richness of the solution manifold, from U(1) (the circle S1) in the one-dimensional case to U ...
R, Simon, K B, Wolf
openaire   +2 more sources

Fractionalization of Fourier transform

Optics Communications, 1995
The conventional definition of fractional-order Fourier transform is demonstrate to be not unique. The same rules can be applied to create a new type of fractional-order Fourier transform which results in a smooth transition of a function when transformed between the real and Fourier spaces.
openaire   +1 more source

Discrete and finite fractional Fourier transforms

Frontiers in Optics, 2003
Finite models for oscillator or waveguide systems provide corresponding fractional Fourier-type transforms between finite arrays of ‘sensor’ points. The kernel matrices are unitary and are well-known in group theory; they involve the discrete polynomials of Kravchuk, q-Kravchuk, Meixner and Hahn.
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Classical versus complex fractional Fourier transformation

Journal of the Optical Society of America A, 2009
The quantum optical complex fractional Fourier transform (FRFT) has been related to the classical FRFT using both classical and quantum formalisms. In particular, it was shown that the kernel of the complex FRFT can be classically produced with rotated astigmatic optical systems that mimic the quantum entanglement property.
openaire   +2 more sources

Persistence in per capita energy consumption: A fractional integration approach with a Fourier function

Energy Economics, 2020
Seref Bozoklu   +2 more
exaly  

Fractional Fourier transforms and their optical implementation II

Journal of the Optical Society of America A: Optics and Image Science, and Vision, 1993
David Mendlovic
exaly  

A Fourier method for the fractional diffusion equation describing sub-diffusion

Journal of Computational Physics, 2007
Chang-Ming Chen, Fawang Liu
exaly  

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