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A reformulation of weighted fractional Fourier transform
Digital Signal Processing, 2020Abstract This paper investigates a class of weighted-type fractional Fourier transform (WFRFT), which is mainly used in signal processing and image encryption. To date, studies have primarily focused on the application of WFRFT, and few studies have examined its properties in detail.
Tieyu Zhao +3 more
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Fractional fourier transform: photonic implementation
Applied Optics, 1994The family of fractional Fourier transforms permits presentation of a temporal signal not only as a function of time or as a pure frequency function but also as a mixed time and frequency function with a continuous degree of emphasis on time or on frequency features.
A W, Lohmann, D, Mendlovic
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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.
Bruce J. West +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.
Bruce J. West +2 more
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Beamforming using the fractional fourier transform
IEEE Transactions on Signal Processing, 2003We present a new method of beamforming using the fractional Fourier transform (FrFT). This method encompasses the conventional minimum mean-squared error (MMSE) beamforming in the frequency domain or spatial domain as special cases. It is especially useful for applications involving chirp signals such as signal enhancement problems with accelerating ...
Imam Samil Yetik, Arye Nehorai
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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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Fractional Fourier–Jacobi type transform
ANNALI DELL'UNIVERSITA' DI FERRARA, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The multiple-parameter fractional Fourier transform
Science in China Series F: Information Sciences, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jun Lang +3 more
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A class of fractional integral transforms: a generalization of the fractional Fourier transform
IEEE Transactions on Signal Processing, 2002The paper presents a systematic and unified approach to fractional integral transforms. We introduce a new class of fractional integral transforms that includes the fractional Fourier and Hankel transforms and the fractional integration and differentiation operators as special cases. These fractional transforms may also be viewed as angular transforms,
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A sparse approximation for fractional Fourier transform
Advances in Computational MathematicsThis papers deals with the fractional Fourier transform of the form for \(\alpha\in[-\pi,\pi]\): \[ \wedge_{\alpha}f(\xi) := \int_{\mathbb{R}} K_{\alpha}(x,\xi)f(x)dx, \quad f\in\mathcal{S}(\mathbb{R}), \] where the kernel \(K_{\alpha}(x,\xi)\) is defined as follows \[ K_{\alpha}(x,\xi) := \left\{ \begin{array}{ll} \displaystyle A_{\alpha}\mathrm{exp ...
Fang Yang +3 more
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Deep Fractional Fourier Transform
Advances in Neural Information Processing Systems 36, 2023Hu Yu +4 more
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