The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
08 Mar 1998-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 454, Iss: 1971, pp 903-995
TL;DR: In this paper, a new method for analysing nonlinear and nonstationary data has been developed, which is the key part of the method is the empirical mode decomposition method with which any complicated data set can be decoded.
Abstract: A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the empirical mode decomposition method with which any complicated data set can be dec...
Citations
More filters
TL;DR: The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF.
Abstract: A new Ensemble Empirical Mode Decomposition (EEMD) is presented. This new approach consists of sifting an ensemble of white noise-added signal (data) and treats the mean as the final true result. Finite, not infinitesimal, amplitude white noise is necessary to force the ensemble to exhaust all possible solutions in the sifting process, thus making the different scale signals to collate in the proper intrinsic mode functions (IMF) dictated by the dyadic filter banks. As EEMD is a time–space analysis method, the added white noise is averaged out with sufficient number of trials; the only persistent part that survives the averaging process is the component of the signal (original data), which is then treated as the true and more physical meaningful answer. The effect of the added white noise is to provide a uniform reference frame in the time–frequency space; therefore, the added noise collates the portion of the signal of comparable scale in one IMF. With this ensemble mean, one can separate scales naturall...
6,437 citations
TL;DR: This work proposes an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently and is a generalization of the classic Wiener filter into multiple, adaptive bands.
Abstract: During the late 1990s, Huang introduced the algorithm called Empirical Mode Decomposition, which is widely used today to recursively decompose a signal into different modes of unknown but separate spectral bands. EMD is known for limitations like sensitivity to noise and sampling. These limitations could only partially be addressed by more mathematical attempts to this decomposition problem, like synchrosqueezing, empirical wavelets or recursive variational decomposition. Here, we propose an entirely non-recursive variational mode decomposition model, where the modes are extracted concurrently. The model looks for an ensemble of modes and their respective center frequencies, such that the modes collectively reproduce the input signal, while each being smooth after demodulation into baseband. In Fourier domain, this corresponds to a narrow-band prior. We show important relations to Wiener filter denoising. Indeed, the proposed method is a generalization of the classic Wiener filter into multiple, adaptive bands. Our model provides a solution to the decomposition problem that is theoretically well founded and still easy to understand. The variational model is efficiently optimized using an alternating direction method of multipliers approach. Preliminary results show attractive performance with respect to existing mode decomposition models. In particular, our proposed model is much more robust to sampling and noise. Finally, we show promising practical decomposition results on a series of artificial and real data.
4,111 citations
Cites background or methods from "The empirical mode decomposition an..."
...Despite the limited mathematical understanding and some obvious shortcomings, the EMDmethod has had significant impact and is widely used in a broad variety of time-frequency analysis applications....
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...Index Terms—AM-FM, augmented Lagrangian, Fourier transform, Hilbert transform, mode decomposition, spectral decomposition, variational problem, Wiener filter....
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TL;DR: It turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions, and the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.
Abstract: Empirical mode decomposition (EMD) has recently been pioneered by Huang et al. for adaptively representing nonstationary signals as sums of zero-mean amplitude modulation frequency modulation components. In order to better understand the way EMD behaves in stochastic situations involving broadband noise, we report here on numerical experiments based on fractional Gaussian noise. In such a case, it turns out that EMD acts essentially as a dyadic filter bank resembling those involved in wavelet decompositions. It is also pointed out that the hierarchy of the extracted modes may be similarly exploited for getting access to the Hurst exponent.
2,304 citations
TL;DR: In this paper, Hilbert spectral analysis is proposed as an alternative to wavelet analysis, which provides not only a more precise definition of particular events in time-frequency space, but also more physically meaningful interpretations of the underlying dynamic processes.
Abstract: We survey the newly developed Hilbert spectral analysis method and its applications to Stokes waves, nonlinear wave evolution processes, the spectral form of the random wave field, and turbulence. Our emphasis is on the inadequacy of presently available methods in nonlinear and nonstationary data analysis. Hilbert spectral analysis is here proposed as an alternative. This new method provides not only a more precise definition of particular events in time-frequency space than wavelet analysis, but also more physically meaningful interpretations of the underlying dynamic processes.
1,945 citations
Cites background or methods from "The empirical mode decomposition an..."
...As discussed in Huang et al (1998a), such a definition gives only a global averaged meaning to the energy and time scales....
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...(7) The procedure is illustrated in Huang et al (1998a)....
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...We will introduce the whole process by starting from the Hilbert transform....
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...31 :4 by C A L IF O R N IA I N ST IT U T E P1: KKK/NBL/spd/mbg P2: NBL/ARY QC: NBL/kba T1: NBL November 24, 1998 12:47 Annual Reviews AR075-12...
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...A degree of statistical stationarity is also defined by Huang et al (1998a)....
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TL;DR: A plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention, and implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.
Abstract: Synchronous rhythms represent a core mechanism for sculpting temporal coordination of neural activity in the brain-wide network. This review focuses on oscillations in the cerebral cortex that occur during cognition, in alert behaving conditions. Over the last two decades, experimental and modeling work has made great strides in elucidating the detailed cellular and circuit basis of these rhythms, particularly gamma and theta rhythms. The underlying physiological mechanisms are diverse (ranging from resonance and pacemaker properties of single cells to multiple scenarios for population synchronization and wave propagation), but also exhibit unifying principles. A major conceptual advance was the realization that synaptic inhibition plays a fundamental role in rhythmogenesis, either in an interneuronal network or in a reciprocal excitatory-inhibitory loop. Computational functions of synchronous oscillations in cognition are still a matter of debate among systems neuroscientists, in part because the notion of regular oscillation seems to contradict the common observation that spiking discharges of individual neurons in the cortex are highly stochastic and far from being clocklike. However, recent findings have led to a framework that goes beyond the conventional theory of coupled oscillators and reconciles the apparent dichotomy between irregular single neuron activity and field potential oscillations. From this perspective, a plethora of studies will be reviewed on the involvement of long-distance neuronal coherence in cognitive functions such as multisensory integration, working memory, and selective attention. Finally, implications of abnormal neural synchronization are discussed as they relate to mental disorders like schizophrenia and autism.
1,774 citations
References
More filters
TL;DR: In this paper, the authors examined the natural representation of a signal through the dynamic time and frequency properties of its energy distribution and proposed a heuristic approach for resolving the inverse problem in physical systems.
Abstract: Various decomposition techniques have been employed in signal processing for exploiting and highlighting the characteristics of a given signal. The approach discussed in this paper, conceived from the observation of wave packets in scattering phenomena, is to examine the natural representation of a signal through the dynamic time and frequency properties of its energy distribution. For a time‐varying signal from a physical system with finite energy content, the selected natural frame component functions, which may not be necessarily orthogonal, can form a complete set for the particular signal under analysis. The decomposition with these nonorthogonal frames then becomes optimal and unique. Algorithms for evaluating the composition of this type of frame are derived from the coherence property of the given signal and image processing is used to estimate the approximate form of needed functions. A simulated multimode signal and the response of the scattered wave signature from an isolated spherical shell are examples used to illustrate a heuristic approach, based on this decomposition method, for resolving the inverse problem in physical systems.
15 citations
"The empirical mode decomposition an..." refers methods in this paper
...An extension of this method has been made by Yen (1994), who used the Wigner–Ville distribution to define wave packets that reduce Proc....
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...An extension of this method has been made by Yen (1994) , who used the Wigner{Ville distribution to dene wave packets that reduce...
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TL;DR: The Mexico Valley earthquake of 1985 was devastating and the extent of the damage is attributed to the very exceptional and extreme geological and topological conditions in the area as mentioned in this paper, where significant attention was focussed on the role played by the top soft layer.
14 citations
"The empirical mode decomposition an..." refers background in this paper
...Hadley et al. (1991) studied such a case and attributed the peakiness to soil-induced amplification of the ground motion....
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...The new Hilbert spectral analysis has clearly identified the new oscillation mode similar to the case studied by Hadley et al. (1991) but from a different cause....
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Book•
01 Jan 1994
TL;DR: The digital anti-alias filter for linear time invariant systems and deconvolution, a glimpse ahead.
Abstract: RC filter- General linear time invariant systems- The seismometer- The sampling process- Analog to digital conversion- From infinitely continuous to finite discrete- The digital anti-alias filter- Deconvolution, a glimpse ahead
13 citations
01 May 1995
TL;DR: In this article, a spatial integration filtering method is applied to process 4.5 years of Geosat altimeter sea level anomalies (SLA) recorded from 1 April 1985 to 17 September 1989.
Abstract: A spatial integration filtering method is applied to process 4.5 years of Geosat altimeter sea level anomalies(SLA) recorded from 1 April 1985 to 17 September 1989. The integral limits are chosen as ±1.5° latitude centered at the equator and ±4° longitude centered at the each central longitude. These limits are chosen in order to eliminate the random noise and to enhance the equatorially trapped wave signals. The spatial-integration-filtered SLA time series show periodical signals with different time scales. Processing the SLA time series with a Short Time Fourier Transform (STFT) yields the time-frequency spectra of the SLA which show a frequency spectral splitting-combining phenomenon in the periods during and after the 1986–1987 El Ninio-Southern Oscillation (ENSO) event. Analysis of non-linear wave-wave interaction indicates that this phenomenon results from amplitude modulation of the short period oscillations in the 60–100 day band by a long period oscillation with a period of about 500 days. The wave components of the short period oscillations are further analysed using the equatorial wave modes to fit the meridional distribution of the SLA. The results indicate that the downwelling Kelvin wave mode before and during the peak phase of 1986–1987 ENSO and the upwelling Kelvin wave mode during the 1988 La Nina are the dominant components. The first and second Rossby wave modes play important roles for entire time series and occasionally become the dominant components. The mean phase speed of Kelvin wave mode during the 1986–1987 ENSO is 3.0 m s−1 which is 25% higher than those in non-ENSO periods.
10 citations
"The empirical mode decomposition an..." refers background or methods in this paper
...The dynamics of the equatorial Kelvin waves have been discussed extensively by Zheng et al. (1995)....
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...The accepted view of the equatorial dynamics is the propagation of Kelvin waves forced by variable wind stress (Byod 1980; Zheng et al. 1995)....
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...Because of the importance of the equatorial region in determining the global climate pattern, the altimeter data have been used extensively to study the dynamics of this area (Miller et al. 1988; Miller & Cheney 1990; Zheng et al. 1994, 1995)....
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TL;DR: In this paper, the spatial distribution of geostrophic eddy kinetic energy and examples of a synoptic map of the eddy field (April 1977) and of a time series at a point were compared to and synthesized with a diverse and select set of existing measurements and observations obtained in situ by a variety of instrumental techniques.
Abstract: Altimeter data obtained from GEOS-3 during the three year period 1975-78 for a region of the western North Atlantic which includes a portion of the Gulf Stream system and part of the open ocean area of the subtropical gyre are analyzed by a new technique which utilizes all the points along the satellite tracks. The physical phenomenon studied are the time-variable but almost geostrophic currents, or mesoscale eddies, so that geoid errors contaminate the scientific signal minimally and the dynamical interpretation is direct. Results presented include the spatial distribution of geostrophic eddy kinetic energy and examples of a synoptic map of the eddy field (April 1977) and of a time series at a point. These results are compared to and synthesized with a diverse and select set of existing measurements and observations obtained in situ by a variety of instrumental techniques. The agreement is generally good, and the altimeter data analyzed provides new information on features in the map of mean eddy kinetic energy. The implications are that satellite altimetry will serve as a powerful quantitative tool in eddy current research and that even presently archived data contains further useful scientific information.
10 citations
"The empirical mode decomposition an..." refers methods in this paper
...(iv) Altimeter data from the equatorial ocean Satellite altimetry has been a powerful technique for large scale ocean circulation studies (Huang et al. 1978; Robinson et al. 1983)....
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