Hilbert–Huang Transform and Its Applications

Huang, Norden E.; Shen, Samuel S. P.

doi:10.1142/8804

Cited by 578 publications

(367 citation statements)

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“…Reynolds-dependent) intermittent corrections. Other analysing tools which have proved to be optimal to reduce non-local effects, such as the Hilbert-Huang transform (Huang & Shen 2005), may also help to better clarify this point. If intermittency in the helical cascade is confirmed, it will be important to study it in a more quantitative way in order to understand similarities to and differences from the corresponding phenomenon observed for the whole NS dynamics with all triads included and in the presence of rotation (Mininni et al 2009).…”

Section: Direct Helicity Cascadementioning

confidence: 99%

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

2013

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We investigate the transfer properties of energy and helicity fluctuations in fully developed homogeneous and isotropic turbulence by changing the nature of the nonlinear Navier-Stokes terms. We perform a surgery of all possible interactions, by keeping only those triads that have sign-definite helicity content. In order to do this, we apply an exact decomposition of the velocity field in a helical Fourier basis, as first proposed by Constantin & Majda (Commun. Math. Phys, vol. 115, 1988, p. 435) and exploited in great detail by Waleffe (Phys. Fluids A, vol. 4, 1992, p. 350), and we evolve the Navier-Stokes dynamics keeping only those velocity components carrying a well-defined (positive or negative) helicity. The resulting dynamics preserves translational and rotational symmetries but not mirror invariance. We give clear evidence that this three-dimensional homogeneous and isotropic chiral turbulence is characterized by a stationary inverse energy cascade with a spectrum E back (k) ∼ k −5/3 and by a direct helicity cascade with a spectrum E forw (k) ∼ k −7/3 . Our results are important to highlight the dynamics and statistics of those subsets of all possible Navier-Stokes interactions responsible for reversal events in the energy-flux properties, and demonstrate that the presence of an inverse energy cascade is not necessarily connected to a two-dimensionalization of the flow. We further comment on the possible relevance of such findings to flows of geophysical interest under rotations and in thin layers. Finally we propose other innovative numerical experiments that can be achieved by using a similar decimation of degrees of freedom.

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Section: Direct Helicity Cascadementioning

confidence: 99%

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

2013

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“…As expected, each consecutive IMF had characteristically lower frequencies. It can also be observed that, although a summation of the IMFs and the residue results in the input signal, the IMFs and the residue extracted do not have the slightest propensity towards linearity, stationarity nor time-invariance (Echeverria et al, 2001;Huang and Shen, 2005;Shi and Law, 2007). This approach to signal decomposition is effectively dynamic and is void of a priori assumptions of the characteristics of the input data.…”

Section: Signal Decomposition and Noise Extractionmentioning

confidence: 99%

Powerline noise elimination in neural signals via blind source separation and wavelet analysis

Akwei-Sekyere

2014

Preprint

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The distortion of neural signals by powerline noise from recording biomedical devices has the potential to reduce the quality and convolute the interpretations of neural data. State of the art electrophysiology employs band-stop filters with which powerline noise are attenuated to low-amplitudes. Due to the instability of neural signals, the distribution of signals filtered out may not be centered at \(50/60Hz\). As a result, self-correction methods are needed to optimize the performance of these filters. Since powerline noise is additive in nature, it is intuitive to model powerline noise in a raw electrophysiological recording and subtract it from the raw data in order to obtain neural data. This paper proposes a method that utilizes this approach by decomposing the recorded signal and extracting powerline noise via blind source separation and wavelet analysis. The performance of this algorithm was compared with that of a band-stop finite impulse response filter. The proposed method was able to expel sinusoidal signals within powerline noise frequency range with higher fidelity in comparison with the mentioned band-stop finite impulse response filter, especially at low signal-to-noise ratio. ABSTRACTThe distortion of neural signals by powerline noise from recording biomedical devices has the potential to reduce the quality and convolute the interpretations of neural data. State of the art electrophysiology employs band-stop filters with which powerline noise are attenuated to low-amplitudes. Due to the instability of neural signals, the distribution of signals filtered out may not be centered at 50/60Hz. As a result, self-correction methods are needed to optimize the performance of these filters. Since powerline noise is additive in nature, it is intuitive to model powerline noise in a raw electrophysiological recording and subtract it from the raw data in order to obtain neural data. This paper proposes a method that utilizes this approach by decomposing the recorded signal and extracting powerline noise via blind source separation and wavelet analysis. The performance of this algorithm was compared with that of a band-stop finite impulse response filter. The proposed method was able to expel sinusoidal signals within powerline noise frequency range with higher fidelity in comparison with the mentioned band-stop finite impulse response filter, especially at low signal-to-noise ratio.

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“…Empirical mode decomposition (EMD) [1] is a technique specially developed for analyzing various kinds of non-stationary signals. Its uniqueness, power and effectiveness have already been demonstrated by its successful applications to many important problems encountered in processing biomedical, financial, geographical, acoustic, vibrational, hydroacoustic and other types of signals.…”

Section: Introductionmentioning

confidence: 99%

“…Otherwise, the IMF extraction is terminated and a final monotonous residual is formed. The two necessary conditions a function must satisfy in order to be counted as an IMF are as follows [1]:…”

Section: Introductionmentioning

confidence: 99%

New approaches to pattern discovery in signals via empirical mode decomposition

Klionskiy¹,

Kupriyanov²,

Kaplun³

et al. 2017

Vib. proced.

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Empirical mode decomposition (EMD) is an adaptive, data-driven technique for processing and analyzing various types of non-stationary vibrational signals. EMD is a powerful and effective tool for signal preprocessing (denoising, detrending, regularity estimation) and time-frequency analysis. This paper discusses pattern discovery in signals via EMD. New approaches to this problem are introduced. In addition, the methods expounded here may be considered as a way of denoising and coping with the redundancy problem of EMD. A general classification of intrinsic mode functions (IMFs) in accordance with their physical interpretation is offered and an attempt is made to perform classification on the basis of the regression theory, special classification statistics and a clustering algorithm. The main advantage of the suggested techniques is their capability of working automatically. Simulation studies have been undertaken on multiharmonic vibrational signals.

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Hilbert–Huang Transform and Its Applications

Cited by 578 publications

References 0 publications

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

Powerline noise elimination in neural signals via blind source separation and wavelet analysis

New approaches to pattern discovery in signals via empirical mode decomposition

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