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Trainable Fractional Fourier Transform
IEEE Signal Processing LettersRecently, the fractional Fourier transform (FrFT) has been integrated into distinct deep neural network (DNN) models such as transformers, sequence models, and convolutional neural networks (CNNs).
E. Koç +3 more
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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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Wigner distribution and fractional Fourier transform
Proceedings of the Sixth International Symposium on Signal Processing and its Applications (Cat.No.01EX467), 2002We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform.
MJ Martin Bastiaans, Tatiana Alieva
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The fractional Fourier transform and time-frequency representations
IEEE Transactions on Signal Processing, 1994The functional Fourier transform (FRFT), which is a generalization of the classical Fourier transform, was introduced a number of years ago in the mathematics literature but appears to have remained largely unknown to the signal processing community, to ...
L. B. Almeida
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IEEE Geoscience and Remote Sensing Letters, 2020
In this letter, a novel fast detection algorithm, known as robust sparse fractional Fourier transform (RSFRFT), is proposed for low-observable maneuvering target detection in a clutter background.
Xiaohan Yu +3 more
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In this letter, a novel fast detection algorithm, known as robust sparse fractional Fourier transform (RSFRFT), is proposed for low-observable maneuvering target detection in a clutter background.
Xiaohan Yu +3 more
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2003
In the next few lectures we provide a brief overview of Fourier analysis and how it has been used to model lin- ear physical phenomena, particularly the reversible propagation of scalar waves in homogeneous media and the irreversible diffusion of one molecular species within another.
Paolo Grigolini +2 more
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In the next few lectures we provide a brief overview of Fourier analysis and how it has been used to model lin- ear physical phenomena, particularly the reversible propagation of scalar waves in homogeneous media and the irreversible diffusion of one molecular species within another.
Paolo Grigolini +2 more
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The fractional Fourier transform on graphs
2017 Asia-Pacific Signal and Information Processing Association Annual Summit and Conference (APSIPA ASC), 2017The emerging field of signal processing on graphs merges algebraic or spectral graph theory with discrete signal processing techniques to process signals on graphs. In this paper, a definition of the fractional Fourier transform on graphs (GFRFT) is proposed and consolidated, which extends the discrete fractional Fourier transform (DFRFT) in the same ...
Yiqian Wang, Qi-yuan Cheng, Bing-Zhao Li
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Wavelet-fractional Fourier transforms [PDF]
Chinese Physics B, 2008 This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite–Gaussian functions. The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
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Fractional Fourier–Kravchuk transform
Journal of the Optical Society of America A, 1997We introduce a model of multimodal waveguides with a finite number of sensor points. This is a finite oscillator whose eigenstates are Kravchuk functions, which are orthonormal on a finite set of points and satisfy a physically important difference equation.
Natig M. Atakishiyev, Kurt Bernardo Wolf
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Multidimensional fractional Fourier transform and generalized fractional convolution
Integral transforms and special functions, 2020In this paper, we prove inversion theorems and Parseval identity for the multidimensional fractional Fourier transform. Analogous to the existing fractional convolutions on functions of single variable, we also introduce a generalized fractional ...
R. Kamalakkannan, R. Roopkumar
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