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The Fractional Hilbert Transform of Generalized Functions [PDF]
The fractional Hilbert transform, a generalization of the Hilbert transform, has been extensively studied in the literature because of its widespread application in optics, engineering, and signal processing. In the present work, we expand the fractional
Saleem Iqbal
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A Bayesian view on the Hilbert transform and the Kramers-Kronig transform of electrochemical impedance data: Probabilistic estimates and quality scores [PDF]
Electrochemical impedance spectroscopy (EIS) is one of the most widely used experimental tools in electrochemistry and has applications ranging from energy storage and power generation to medicine. Considering the broad applicability of the EIS technique,
Liu Jiapeng +2 more
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Optics Letters, 1996
We have generalized the Hilbert transform by defining the fractional Hilbert transform (FHT) operation. In the first stage, two different approaches for defining the FHT are suggested. One is based on modifying only the spatial filter, and the other proposes using the fractional Fourier plane for filtering.
A W, Lohmann, D, Mendlovic, Z, Zalevsky
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We have generalized the Hilbert transform by defining the fractional Hilbert transform (FHT) operation. In the first stage, two different approaches for defining the FHT are suggested. One is based on modifying only the spatial filter, and the other proposes using the fractional Fourier plane for filtering.
A W, Lohmann, D, Mendlovic, Z, Zalevsky
openaire +2 more sources
On the Approximability of the Hilbert Transform
2018 IEEE International Symposium on Information Theory (ISIT), 2018It was recently shown that on a large class of important Sobolev-like Banach spaces there exist no linear methods which are able to approximate the Hilbert transform from samples of the given function. This implies that there exists no linear algorithm for calculating the Hilbert transform which can be implemented on a digital computer and which ...
Holger Boche, Volker Pohl
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Chinese Annals of Mathematics, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Jiecheng, Ding, Yong, Fan, Dashan
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Chen, Jiecheng, Ding, Yong, Fan, Dashan
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2023
AbstractThis chapter emphasizes the Hilbert-space properties of these operators. In particular, we study the boundedness, norm, adjoint, and spectral properties of Hilbert transforms and how these properties relate to harmonic conjugation and Riemann–Hilbert problems.
Stephan Ramon Garcia +2 more
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AbstractThis chapter emphasizes the Hilbert-space properties of these operators. In particular, we study the boundedness, norm, adjoint, and spectral properties of Hilbert transforms and how these properties relate to harmonic conjugation and Riemann–Hilbert problems.
Stephan Ramon Garcia +2 more
openaire +1 more source

