An extended Hilbert transform method for reconstructing the phase from an oscillatory signal [PDF]
Scientific Reports, 2023 Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed signals.
Akari Matsuki +2 more
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A Frequency Estimation Scheme Based on Gaussian Average Filtering Decomposition and Hilbert Transform: With Estimation of Respiratory Rate as an Example [PDF]
Sensors, 2023 Frequency estimation plays a critical role in vital sign monitoring. Methods based on Fourier transform and eigen-analysis are commonly adopted techniques for frequency estimation.
Yue-Der Lin +3 more
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The Atkinson Theorem in Hilbert C*-Modules over C*-Algebras of Compact Operators [PDF]
Abstract and Applied Analysis, 2007 The concept of unbounded Fredholm operators on Hilbert C*-modules over an arbitrary C*-algebra is discussed and the Atkinson theorem is generalized for bounded and unbounded Feredholm operators on Hilbert C*-modules over C*-algebras of compact operators.
A. Niknam, K. Sharifi
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Surveys in Mathematics and its Applications, 2021 The Hilbert transform is essentially the only singular operator in one dimension. This undoubtedly make it one of the most important linear operator in harmonic analysis.
Edisson Arley Arcos +1 more
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Double-exposure optical sectioning structured illumination microscopy based on Hilbert transform reconstruction. [PDF]
PLoS One, 2015 Structured illumination microscopy (SIM) with axially optical sectioning capability has found widespread applications in three-dimensional live cell imaging in recent years, since it combines high sensitivity, short image acquisition time, and high ...
Zhou X +10 more
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One result on boundedness of the Hilbert transform in Marcinkiewics spaces
Вестник КазНУ. Серия математика, механика, информатика, 2022 In mathematics and in signal theory, the Hilbert transform is an important linear operator that takes a real-valued function and produces another real-valued function.
Nurken Tursynbayuly Bekbayev +1 more
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Quadratic-Phase Hilbert Transform and the Associated Bedrosian Theorem
Axioms, 2023 The Hilbert transform is a commonly used linear operator that separates the real and imaginary parts of an analytic signal and is employed in various fields, such as filter design, signal processing, and communication theory.
Hari M. Srivastava +4 more
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Approximation of the Hilbert transform in the Lebesgue spaces
Journal of Numerical Analysis and Approximation Theory, 2023 The Hilbert transform plays an important role in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the ...
Rashid Aliev, Lale Alizade
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Inequalities for a generalized finite Hilbert transform of convex functions [PDF]
Mathematica Moravica, 2021 In this paper we obtain some new inequalities for a generalized finite Hilbert transform of convex functions. Applications for particular instances of finite Hilbert transforms are given as well.
Dragomir Silvestru Sever
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