Hilbert Envelope Extraction from Real Discrete Finite Signals Considering the Nonlocality of Hilbert Transform

2020 ◽  
Author(s):  
Ponomareva Olga ◽  
Ponomarev Alexey ◽  
Smirnova Natalia
Keyword(s):  
Hilbert Transform ◽  
Hilbert Envelope ◽  
Envelope Extraction

scholarly journals The condition monitoring of diesel engines using acoustic signal analysis

2019 ◽  
Vol 13 (1) ◽  
pp. 179
Author(s):  
Widi Prasetyo ◽  
Mudrik Alaydrus
Keyword(s):  
Fourier Transform ◽  
Hilbert Transform ◽  
Acoustic Signal ◽  
Signal Analysis ◽  
Scientific Basis ◽  
Frequency Pattern ◽  
A Value ◽  
Acoustic Signal Analysis ◽  
Envelope Extraction ◽  
Engine Condition

<span>Engine have become one of the supportive asset for many activity and work, therefore engine need attention for its condition. The easiest way to do is through the acoustic sound of the engine itself. Most of the time, the engine sounds are checked using a traditional way that may causing a debate regarding its condition. This is due to no supportive scientific basis to know about engine condition using their own acoustic sound. A value from its frequency pattern is needed as scientific basis to determine an engine condition using acoustic sound. Method of envelope extraction by hilbert transform, fast fourier transform, and correlation coefficient are used to find that value. A series of tests have been carried out on the values that have been found and the result are promising for telling engine condition, but unfortunately the values has not been able to identify type of damage that occur on the engine.</span>

Envelope Extraction Algorithms and the Application in Motor Imagery

2013 ◽  
Vol 401-403 ◽  
pp. 1551-1554
Author(s):  
Xiao Xiao Gong ◽  
Xiao Pei Wu ◽  
Xiao Jing Guo ◽  
Lei Zhang
Keyword(s):  
Motor Imagery ◽  
Hilbert Transform ◽  
Sliding Window ◽  
Signal Denoising ◽  
Eeg Signals ◽  
Envelope Detection ◽  
Application Potential ◽  
Left And Right ◽  
Envelope Extraction ◽  
Eeg Signal Processing

The envelope information is an important feature in EEG signal processing. This paper analyses the application of Hilbert transform and sliding window Infomax algorithm in envelope detection of EEG signals from different respects, and compares the classification results in left and right hand motor imagery. From the results, we see that, the signal envelope extracted by Hilbert transform is more accurate than sliding window Infomax algorithm, but the latter is superior in signal denoising, real-time ability and the richness of characteristics, sliding window Infomax algorithm has greater application potential.

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

2020 ◽  
Vol 2020 (48) ◽  
pp. 17-24
Author(s):  
I.M. Javorskyj ◽  
◽  
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.

A Bayesian View on the Hilbert Transform and the Kramers-Kronig Transform of Electrochemical Impedance Data: Probabilistic Estimates and Quality Scores

2020 ◽  
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>

Display of Hilbert Transform Using Polarization Filter

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

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

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.

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

Mathematics ◽  
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.

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

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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