The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Citations
152 citations
152 citations
Cites methods from "The empirical mode decomposition an..."
...[7] gives the full treatment of the HHT method....
[...]
...Two stopping criteria have been proposed: a Cauchy-type convergence that depends on limiting the standard deviation computed from two consecutive IMFs [7], and one that depends on the agreement of the numbers of extrema and zero crossings [8]....
[...]
152 citations
152 citations
Cites background or methods from "The empirical mode decomposition an..."
...EMD and EEMD have been shown to be able to extract nonlinear trends in climatic time series (e.g., Huang et al. 1998; Wu et al. 2007; Wu and Huang 2009; Wu et al. 2011; Franzke 2009, 2010; Franzke and Woollings 2011; Qian et al. 2011)....
[...]
...…when the distribution of the residuals is nonGaussian and known. d. EEMD The Ensemble Empirical Mode Decomposition method (Wu and Huang 2009; Huang et al. 1998; Huang and Wu 2008; Wu et al. 2007; Qian et al. 2009; Franzke 2010) decomposes a time series into a finite number of intrinsic mode…...
[...]
...First the robustness and accuracy of various trend detection methods are examined: ordinary least squares, robust and generalized linear model regression, Ensemble Empirical Mode Decomposition (EEMD), and wavelets....
[...]
...Also, the EEMD trends are nonlinear and very similar to the cubic fits (Fig....
[...]
...In practice, the algorithm has to be refined by a so-called sifting process (e.g., Huang et al. 1998), which amounts to iterating steps (i)–(iii) until this can be considered a zero mean to some stopping criterion (Huang et al. 1998; Rilling et al. 2003)....
[...]
152 citations
Cites background or methods from "The empirical mode decomposition an..."
...The discrete HT is calculated by utilising transfer function and the DFT [17]....
[...]
...2, pp. 388-397 © The Institution of Engineering and Technology 2017 391 The discretise transform transfer function is described as H(ω) = −J 0 ω π 0 ω = 0 and ω = π J − π ω 0 (10) The discrete HT is calculated by utilising transfer function and the DFT [17]....
[...]
...The range of SD value is considered as 0.2–0.3 as rightly suggested by Huang and Shen [17], for the shifting process of difference between two consecutive shifting....
[...]
...The complete procedure for applying HT is given below: Step 1: Apply DFT to the signal S(k). where, k = 1, 2… ....
[...]
...As stated by Huang and Shen in [17], an IMF is presented as a function that fulfils the succeeding two preconditions:...
[...]
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)....
[...]