Determination of fundamental asteroseismic parameters using the Hilbert transform

abstract Determination of the phase response of a minimum-phase seismic system directly from the amplitude response by the Hilbert transform is investigated. The error by this technique is found to be less than 2° with the major source of inaccuracy being the uncertainties in the amplitude data. This technique is useful for rapid determination of the phase response if the amplitude response is known.

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Determination of Two-Dimensional Correlation Spectra Using the Hilbert Transform

Applied Spectroscopy ◽

10.1366/0003702001950472 ◽

2000 ◽

Vol 54 (7) ◽

pp. 994-999 ◽

Cited By ~ 350

Author(s):

I. Noda

Keyword(s):

Hilbert Transform ◽

Two Dimensional ◽

The Hilbert Transform

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Model of multicomponent narrow-band periodical non-stationary random signal

Information extraction and processing ◽

10.15407/vidbir2020.48.017 ◽

2020 ◽

Vol 2020 (48) ◽

pp. 17-24

Author(s):

I.M. Javorskyj ◽

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R.M. Yuzefovych ◽

P.R. Kurapov ◽

◽

...

Keyword(s):

Time Series ◽

Real Time ◽

Hilbert Transform ◽

Spectral Properties ◽

Narrow Band ◽

Analytic Signal ◽

Random Signal ◽

Hilbert Transformation ◽

The Hilbert Transform

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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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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