Sinc Approximation of Multidimensional Hilbert Transform and Its Applications

The correlation and spectral properties of a multicomponent narrowband periodical non-stationary random signal (PNRS) and its Hilbert transformation are considered. It is shown that multicomponent narrowband PNRS differ from the monocomponent signal. This difference is caused by correlation of the quadratures for the different carrier harmonics. Such features of the analytic signal must be taken into account when we use the Hilbert transform for the analysis of real time series.

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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

10.26434/chemrxiv.12152529 ◽

2020 ◽

Cited By ~ 1

Author(s):

Jiapeng Liu ◽

Ting Hei Wan ◽

Francesco Ciucci

Keyword(s):

Power Generation ◽

Electrochemical Impedance Spectroscopy ◽

Hilbert Transform ◽

Electrochemical Impedance ◽

The Self ◽

Impedance Data ◽

The Hilbert Transform ◽

Validation Tests ◽

Self Consistency ◽

Mathematical Relations

<p>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, it is critical to validate the EIS data against the Hilbert transform (HT) or, equivalently, the Kramers–Kronig relations. These mathematical relations allow one to assess the self-consistency of obtained spectra. However, the use of validation tests is still uncommon. In the present article, we aim at bridging this gap by reformulating the HT under a Bayesian framework. In particular, we developed the Bayesian Hilbert transform (BHT) method that interprets the HT probabilistic. Leveraging the BHT, we proposed several scores that provide quick metrics for the evaluation of the EIS data quality.<br></p>

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HILBERT TRANSFORM AND GAIT ANALYSIS: A NEW METHOD TO EVALUATE GAIT VARIABILITY

Anais do V Congresso Brasileiro de Eletromiografia e Cinesiologia e X Simpósio de Engenharia Biomédica ◽

10.29327/cobecseb.78816 ◽

2018 ◽

Author(s):

G. S. Souza ◽

A. O. Andrade ◽

M. F. Vieira

Keyword(s):

Gait Analysis ◽

Hilbert Transform ◽

Gait Variability ◽

New Method

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Display of Hilbert Transform Using Polarization Filter

Journal of Optics ◽

10.1007/bf03549196 ◽

1989 ◽

Vol 18 (2) ◽

pp. 48-50

Author(s):

Kallol Bhattacharya ◽

D. K. Basu ◽

Ajay Ghosh ◽

A. K. Chakrabortt

Keyword(s):

Hilbert Transform ◽

Polarization Filter

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On the Integrability of the Ergodic Hilbert Transform for A Class of Functions with Equal Absolute Values

Georgian Mathematical Journal ◽

10.1515/gmj.1998.101 ◽

1998 ◽

Vol 5 (2) ◽

pp. 101-106

Author(s):

L. Ephremidze

Keyword(s):

Hilbert Transform ◽

Measure Space ◽

Integrable Function ◽

Finite Measure ◽

Ergodic Transformation ◽

Finite Measure Space ◽

Class Of Functions

Abstract It is proved that for an arbitrary non-atomic finite measure space with a measure-preserving ergodic transformation there exists an integrable function f such that the ergodic Hilbert transform of any function equal in absolute values to f is non-integrable.

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A Radial Basis Function Finite Difference Scheme for the Benjamin–Ono Equation

Mathematics ◽

10.3390/math9010065 ◽

2020 ◽

Vol 9 (1) ◽

pp. 65

Author(s):

Benjamin Akers ◽

Tony Liu ◽

Jonah Reeger

Keyword(s):

Radial Basis Function ◽

Hilbert Transform ◽

Basis Function ◽

Differential Operators ◽

Convergence Rates ◽

Traveling Wave Solutions ◽

Algebraic Decay ◽

Pseudo Differential Operators ◽

Radial Basis ◽

The Hilbert Transform

A radial basis function-finite differencing (RBF-FD) scheme was applied to the initial value problem of the Benjamin–Ono equation. The Benjamin–Ono equation has traveling wave solutions with algebraic decay and a nonlocal pseudo-differential operator, the Hilbert transform. When posed on R, the former makes Fourier collocation a poor discretization choice; the latter is challenging for any local method. We develop an RBF-FD approximation of the Hilbert transform, and discuss the challenges of implementing this and other pseudo-differential operators on unstructured grids. Numerical examples, simulation costs, convergence rates, and generalizations of this method are all discussed.

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Variation inequalities for rough singular integrals and their commutators on Morrey spaces and Besov spaces

Advances in Nonlinear Analysis ◽

10.1515/anona-2020-0187 ◽

2021 ◽

Vol 11 (1) ◽

pp. 72-95

Author(s):

Xiao Zhang ◽

Feng Liu ◽

Huiyun Zhang

Keyword(s):

Hilbert Transform ◽

Besov Spaces ◽

Singular Integrals ◽

Riesz Transform ◽

Morrey Spaces ◽

Riesz Transforms ◽

Rough Kernels ◽

Lebesgue Spaces ◽

Variation Operators

Abstract This paper is devoted to investigating the boundedness, continuity and compactness for variation operators of singular integrals and their commutators on Morrey spaces and Besov spaces. More precisely, we establish the boundedness for the variation operators of singular integrals with rough kernels Ω ∈ Lq (S n−1) (q > 1) and their commutators on Morrey spaces as well as the compactness for the above commutators on Lebesgue spaces and Morrey spaces. In addition, we present a criterion on the boundedness and continuity for a class of variation operators of singular integrals and their commutators on Besov spaces. As applications, we obtain the boundedness and continuity for the variation operators of Hilbert transform, Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators on Besov spaces.

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