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The generalized discrete fractional fourier transforms
IEEE International Conference on Acoustics Speech and Signal Processing, 2002In 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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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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Fractional discreteq-Fourier transforms
Journal of Physics A: Mathematical and Theoretical, 2009The discrete Fourier transform (DFT) matrix has a manifold of fractionalizations that depend on the choice of its eigenbases. One prominent basis is that of Mehta functions; here we examine a family of fractionalizations of the DFT stemming from q-extensions of this basis.
Carlos A Muñoz +2 more
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Image steganography using discrete fractional Fourier transform
2013 International Conference on Intelligent Systems and Signal Processing (ISSP), 2013The Fractional Fourier transform (FrFT), as a generalization of the classical Fourier transform, was introduced many years ago in mathematics literature. For the enhanced computation of fractional Fourier transform, discrete version of FrFT came into existence i.e. DFrFT.
A. Soni, J. Jain, R. Roshan
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The multiple-parameter discrete fractional Fourier transform
IEEE Signal Processing Letters, 2006The discrete fractional Fourier transform (DFRFT) is a generalization of the discrete Fourier transform (DFT) with one additional order parameter. In this letter, we extend the DFRFT to have N order parameters, where N is the number of the input data points.
Pei, Soo-Chang, Hsue, Wen-Liang
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The discrete multiple-parameter fractional Fourier transform
Science China Information Sciences, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lang, Jun, Tao, Ran, Wang, Yue
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FPGA implementation of discrete fractional Fourier transform
2010 International Conference on Signal Processing and Communications (SPCOM), 2010Since decades, fractional Fourier transform has taken a considerable attention for various applications in signal and image processing domain. On the evolution of fractional Fourier transform and its discrete form, the real time computation of discrete fractional Fourier transform is essential in those applications.
M. V. N. V. Prasad +2 more
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Orthogonal Projections and Discrete Fractional Fourier Transforms
2006 IEEE 12th Digital Signal Processing Workshop & 4th IEEE Signal Processing Education Workshop, 2006A summary of results from linear algebra pertaining to orthogonal projections onto subspaces of an inner product space is presented. A formal definition and a sufficient condition for the existence of a fractional transform given a unitary periodic operator is given. Next, using an orthogonal projection formula the class of weighted discrete fractional
M. Ozaydin +3 more
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The Fractional Discrete Fourier Transform
1999A fractional version of the Discrete Fourier Transform or DFT, denoted by the Fractional Discrete Fourier Transform or FDFT for short, is discussed here. First, results of a fractional version of the continuous-time Fourier Transform or CTFT are explored and then parallels are made between the DFT and the CTFT.
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Implementation of quantum discrete fractional Fourier transform
Quantum Information and Measurement (QIM) 2017, 2017In 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 +9 more
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