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Implementation of quantum discrete fractional Fourier transform

Quantum Information and Measurement (QIM) 2017, 2017
In this work we experimentally demonstrate the realization of the discrete fractional Fourier transforms (DFrFT) in both the classical and quantum realm. Our approach is fully integrated and free of bulk optical components.
Markus Gräfe, Steffen Weimann, Armando Perez-Leija, Maxime Lebugle, Robert Keil, René Heilmann, Stefan Nolte, Gregor Weihs, Demetrios N. Christodoulides, Alexander Szameit   +9 more
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Digital computation of the fractional Fourier transform [PDF]

IEEE Transactions on Signal Processing, 1996
An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time.
H M Ozaktas, Orhan Arikan
exaly   +2 more sources

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Fractional discrete Fourier transforms

Optics Letters, 1996
Direct calculation of fractional Fourier transforms from the expressions derived for their optical implementation is laborious. An extension of the discrete Fourier transform would have only O(N(2)) computational complexity. We define such a system, offer a general way to compute the fractional discrete Fourier transform matrix, and numerically ...
Z T, Deng, H J, Caulfield, M, Schamschula   +2 more
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Research progress on discretization of fractional Fourier transform

Science in China Series F: Information Sciences, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ran Tao 0003, Feng Zhang 0011, Yue Wang 0001   +2 more
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The generalized discrete fractional fourier transforms

IEEE International Conference on Acoustics Speech and Signal Processing, 2002
In this paper, we develop the generalized discrete fractional Fourier transform (GDFRFT) by factorizing the generalized discrete Fourier transform (GDFT) matrix. Specifically, the eigenvalues and eigenvectors are presented and then used to define the GDFRFT.
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The analysis of the discrete fractional Fourier transform algorithms

2009 Canadian Conference on Electrical and Computer Engineering, 2009
The discrete formal FRFT is difficult to obtained by the directly sampling the continuous FRFT because the kernel function of the continuous fractional Fourier transform (FRFT) exhibits drastic oscillation and the oscillation amplitude has the distinct difference from the different order of the FRFT.
Qi-Wen Ran, Hai-Ying Zhang, Zhongzhao Zhang, Xuejun Sha   +3 more
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The Analysis of Resolution of the Discrete Fractional Fourier Transform

First International Conference on Innovative Computing, Information and Control - Volume I (ICICIC'06), 2006
The fractional Fourier transform (FRFT) is a unified time-frequency transform that does not suffer from the cross terms and is suitable for processing the non stationary signal. It is required to define the corresponding analysis range and discrete resolution in the FRFT domain in order to apply the FRFT to digital signal processing field.
Bing Deng, Ran Tao 0003
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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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Geometry and dynamics in the fractional discrete Fourier transform

Journal of the Optical Society of America A, 2007
The N x N Fourier matrix is one distinguished element within the group U(N) of all N x N unitary matrices. It has the geometric property of being a fourth root of unity and is close to the dynamics of harmonic oscillators. The dynamical correspondence is exact only in the N-->infinity contraction limit for the integral Fourier transform and its ...
Kurt Bernardo, Wolf, Guillermo, Krötzsch   +1 more
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Discrete Fourier Transforms of Fractional Processes with Econometric Applications [PDF]

, 2023
Abstract The discrete Fourier transform (dft) of a fractional process is studied. An exact representation of the dft is given in terms of the component data, leading to the frequency domain form of the model for a fractional process.
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