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Fractional Fourier transforms in two dimensions
Journal of the Optical Society of America A, 2000We 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
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Fractionalization of Fourier transform
Optics Communications, 1995The 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.
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Discrete and finite fractional Fourier transforms
Frontiers in Optics, 2003Finite 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, 2009The 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.
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Fractional Fourier transforms and their optical implementation II
Journal of the Optical Society of America A: Optics and Image Science, and Vision, 1993David Mendlovic
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A Fourier method for the fractional diffusion equation describing sub-diffusion
Journal of Computational Physics, 2007Chang-Ming Chen, Fawang Liu
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