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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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Hilbert transform associated with the fractional Fourier transform
IEEE Signal Processing Letters, 1998The analytic part of a signal f(t) is obtained by suppressing the negative frequency content of f, or in other words, by suppressing the negative portion of the Fourier transform, f/spl circ/, of f. In the time domain, the construction of the analytic part is based on the Hilbert transform f/spl circ/ of f(t).
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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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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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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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Deep Fractional Fourier Transform
Advances in Neural Information Processing Systems 36, 2023Hu Yu +4 more
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On bandlimited signals with fractional Fourier transform
IEEE Signal Processing Letters, 1996We study bandlimited signals with fractional Fourier transform (FRFT). We show that if a nonzero signal f is bandlimited with FRFT F/sub /spl alpha// for a certain real /spl alpha/, then it is not bandlimited with FRFT F/sub /spl beta// for any /spl beta/ with /spl beta//spl ne//spl plusmn//spl alpha/+n/spl pi/ for any integer n.
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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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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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