The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Citations
1,704 citations
1,573 citations
1,533 citations
Cites background or methods from "The empirical mode decomposition an..."
...[8] The HHT consists of empirical mode decomposition and Hilbert spectral analysis [Huang et al., 1996, 1998, 1999]....
[...]
...[6] The combination of the well-known Hilbert spectral analysis (HAS) and the recently developed empirical mode decomposition (EMD) [Huang et al., 1996, 1998, 1999], designated as the Hilbert-Huang transform (HHT) by NASA, indeed, represents such a paradigm shift of data analysis methodology....
[...]
...To explore the applicability of the Hilbert transform, Huang et al. [1998] showed that a purely oscillatory function (or a monocomponent) with a zero reference level is a necessary condition for the above instantaneous frequency calculation method to work appropriately [Huang et al., 1998]....
[...]
...Indeed, searching for the expression of an arbitrary x(t) in terms of a sum of a small number of purely oscillatory functions of which Hilbert transform–based instantaneous frequencies are physically meaningful was the exact motivation for the early development of EMD [Huang et al., 1998]....
[...]
...…the instantaneous frequency method applied to a sinusoidal function of a constant frequency riding on a nonzero reference level (e.g., coswt + C, where C is a constant) does not yield a constant frequency of w; rather, the obtained frequency bears unexpected fluctuations [Huang et al., 1998]....
[...]
1,517 citations
Cites background or methods from "The empirical mode decomposition an..."
...Ensemble Empirical Mode Decomposition EMD [1] decomposes a signal x(t) into a (usually) small number of Intrinsic Mode Functions (IMFs) or modes....
[...]
...INTRODUCTION Empirical Mode Decomposition (EMD) [1] is an adaptive method introduced to analyze non-linear and non-stationary signals....
[...]
...The method here proposed does not suffer from this difficulty because: (i) each realization of residue plus noise is decomposed until the first mode is reached, and (ii) for the final mode K we use as stopping criterion the one used in EMD [1]....
[...]
1,448 citations
Cites background or methods or result from "The empirical mode decomposition an..."
...Given a signal x(t), the effective algorithm of EMD can be summarized as follows [ 2 ] (see also emd.ppt in [9]): 1. identify all extrema of x(t) 2. interpolate between minima (resp....
[...]
...As an improvement to the criteria that have been considered so far [ 2 ], we propose in emd.m [9] to introduce a new criterion based on 2 thresholds θ1 and θ2, aimed at guaranteeing globally small fluctuations in the mean while taking into account locally large excursions....
[...]
...Huang et al. for adaptively representing nonstationary signals as sums of zero-mean AM-FM components [ 2 ]....
[...]
...Although it often proved remarkably effective [1, 2 , 5, 6, 8], the technique is faced with the difficulty of being essentially defined by an algorithm, and therefore of not admitting an analytical formulation which would allow for a theoretical analysis and performance evaluation....
[...]
...emax(t)) 3. compute the mean m(t )=( emin(t)+emax(t))/2 4. extract the detail d(t )= x(t) − m(t) 5. iterate on the residual m(t) In practice, the above procedure has to be refined by a sifting process [ 2 ] which amounts to first iterating steps 1 to 4 upon the detail signal d(t), until this latter can be considered as zero-mean according to some stopping criterion....
[...]
References
16,554 citations
"The empirical mode decomposition an..." refers background in this paper
...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
[...]
8,808 citations
6,693 citations
"The empirical mode decomposition an..." refers background in this paper
...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
[...]
5,910 citations
"The empirical mode decomposition an..." refers methods in this paper
...In order to obtain meaningful instantaneous frequency, restrictive conditions have to be imposed on the data as discussed by Gabor (1946), Bedrosian (1963) and, more recently, Boashash (1992): for any function to have a meaningful instantaneous frequency, the real part of its Fourier transform has…...
[...]
5,806 citations
"The empirical mode decomposition an..." refers background in this paper
...In general, if more quantitative results are desired, the original skeleton presentation is better; if more qualitative results are desired, the smoothed presentation is better....
[...]
...Therefore, the parameter, ν, defined as N21 −N20 = 1 π2 m4m0 −m22 m2m0 = 1 π2 ν2, (3.7) offers a standard bandwidth measure (see, for example, Rice 1944a, b, 1945a, b; Longuet-Higgins 1957)....
[...]