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: In this article, the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal is quantized by quantization of mean trends and oscillations about the means.
Abstract: This paper is devoted to the quantization of the degree of nonlinearity of the relationship between two biological variables when one of the variables is a complex nonstationary oscillatory signal. An example of the situation is the indicial responses of pulmonary blood pressure (P) to step changes of oxygen tension (ΔpO2) in the breathing gas. For a step change of ΔpO2 beginning at time t1, the pulmonary blood pressure is a nonlinear function of time and ΔpO2, which can be written as P(t-t1 | ΔpO2). An effective method does not exist to examine the nonlinear function P(t-t1 | ΔpO2). A systematic approach is proposed here. The definitions of mean trends and oscillations about the means are the keys. With these keys a practical method of calculation is devised. We fit the mean trends of blood pressure with analytic functions of time, whose nonlinearity with respect to the oxygen level is clarified here. The associated oscillations about the mean can be transformed into Hilbert spectrum. An integration of the square of the Hilbert spectrum over frequency yields a measure of oscillatory energy, which is also a function of time, whose mean trends can be expressed by analytic functions. The degree of nonlinearity of the oscillatory energy with respect to the oxygen level also is clarified here. Theoretical extension of the experimental nonlinear indicial functions to arbitrary history of hypoxia is proposed. Application of the results to tissue remodeling and tissue engineering of blood vessels is discussed.
78 citations
TL;DR: In this paper, a comparative study of the conventional stationary wind speed model and a newly proposed non-stationary model using field measurements is presented, and the differences between, the two wind models are briefly reviewed.
Abstract: We present a comparative study of the conventional stationary wind speed model and a newly proposed non-stationary wind speed model using field measurements. The concept of, and the differences between, the two wind models are briefly reviewed. Wind data recorded by a field measurement system for wind turbulence parameters (FMS-WTP) of 1-year duration are analyzed using the two wind models. Comparisons were made between the wind characteristics obtained from the two models, including hourly mean wind speed, turbulence intensity, the wind spectrum, integral length scale, root coherence function and probability density function. The effects of wind types (monsoon or typhoon), statistical properties (stationary or non-stationary), and surface roughness (open-sea fetch or overland fetch) on wind characteristics are discussed. The comparative study demonstrates that the non-stationary wind model appears to be more appropriate than the conventional stationary wind speed model for characterizing turbulent winds of one-hour duration over complex terrain.
78 citations
Cites background or methods from "The empirical mode decomposition an..."
...To this end, a new data processing method termed the empirical mode decomposition (EMD) is employed ( Huang et al. 1998 )....
[...]
...One attractive feature of EMD, as concluded by Huang et al. (1998) , is that for a time series with a trend, the residue after EMD analysis should follow that trend....
[...]
TL;DR: In this paper, the Hilbert spectra, calculated with the Hilbert Huang transform (HHTT), is used for the characterization of electrochemical noise data in corrosion studies and a highly detailed decomposition of the original current and potential data is provided in time and frequency simultaneously.
78 citations
TL;DR: The proposed algorithm uses a fully data-driven multivariate empirical mode decomposition (MEMD) in order to obtain the mu and beta rhythms from the nonlinear EEG signals to provide an important feature for the classification of the left- and right-hand motor imagery tasks.
Abstract: Recent studies have demonstrated the disassociation between the mu and beta rhythms of electroencephalogram EEG during motor imagery tasks. The proposed algorithm in this paper uses a fully data-driven multivariate empirical mode decomposition MEMD in order to obtain the mu and beta rhythms from the nonlinear EEG signals. Then, the strong uncorrelating transform complex common spatial patterns SUTCCSP algorithm is applied to the rhythms so that the complex data, constructed with the mu and beta rhythms, becomes uncorrelated and its pseudocovariance provides supplementary power difference information between the two rhythms. The extracted features using SUTCCSP that maximize the interclass variances are classified using various classification algorithms for the separation of the left- and right-hand motor imagery EEG acquired from the Physionet database. This paper shows that the supplementary information of the power difference between mu and beta rhythms obtained using SUTCCSP provides an important feature for the classification of the left- and right-hand motor imagery tasks. In addition, MEMD is proved to be a preferred preprocessing method for the nonlinear and nonstationary EEG signals compared to the conventional IIR filtering. Finally, the random forest classifier yielded a high performance for the classification of the motor imagery tasks.
78 citations
Cites methods from "The empirical mode decomposition an..."
...thus empirical mode decomposition was used to produce more accurate narrowband signals compared to the Fourier analysis [41, 42]....
[...]
TL;DR: The proposed denoising and R-peak detection algorithm can effectively eliminate the Gaussian noise, baseline wander, and power-line interference added to the ECG signal and can also function reliably even under poor signal quality and with long P and T peaks.
Abstract: The electrocardiogram (ECG ) signal is prone to various high and low frequency noises, including baseline wandering and power-line interference, which become the source of errors in QRS and in other extracted features. This paper presents a new ECG signal-processing approach based on empirical mode decomposition (EMD) and an improved approximate envelope method. To reduce the number of the initial intrinsic mode functions (IMFs), a Butterworth lowpass filter is used to eliminate high frequency noises before the EMD. To correct baseline wandering and to eliminate low frequency noises, the two last-order IMFs are abandoned. An improved approximate envelope is proposed and applied after the Hilbert transform to enhance the energy of QRS complexes and to suppress unwanted P/T waves and noises. Then, an algorithm based on the slope threshold is used for R-peak detection. The proposed denoising and R-peak detection algorithm are validated using the MIT-BIH Arrhythmia Database. The simulation results show that the proposed method can effectively eliminate the Gaussian noise, baseline wander, and power-line interference added to the ECG signal. The method can also function reliably even under poor signal quality and with long P and T peaks. The QRS detector has an average sensitivity of Se=99.94 % and a positive predictivity of +P=99.87 % over the first lead of the MIT-BIH Arrhythmia Database.
78 citations
References
More filters
TL;DR: In this paper, it was shown that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states, and systems with bounded solutions are shown to possess bounded numerical solutions.
Abstract: Finite systems of deterministic ordinary nonlinear differential equations may be designed to represent forced dissipative hydrodynamic flow. Solutions of these equations can be identified with trajectories in phase space For those systems with bounded solutions, it is found that nonperiodic solutions are ordinarily unstable with respect to small modifications, so that slightly differing initial states can evolve into considerably different states. Systems with bounded solutions are shown to possess bounded numerical solutions.
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....
[...]
Book•
01 Jan 1974
TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.
Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.
8,808 citations
Book•
01 Jan 1971
TL;DR: A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems, is presented in this article.
Abstract: From the Publisher:
A revised and expanded edition of this classic reference/text, covering the latest techniques for the analysis and measurement of stationary and nonstationary random data passing through physical systems. With more than 100,000 copies in print and six foreign translations, the first edition standardized the methodology in this field. This new edition covers all new procedures developed since 1971 and extends the application of random data analysis to aerospace and automotive research; digital data analysis; dynamic test programs; fluid turbulence analysis; industrial noise control; oceanographic data analysis; system identification problems; and many other fields. Includes new formulas for statistical error analysis of desired estimates, new examples and problem sets.
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)....
[...]
01 Jan 1946
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…...
[...]
TL;DR: In this paper, the authors used the representations of the noise currents given in Section 2.8 to derive some statistical properties of I(t) and its zeros and maxima.
Abstract: In this section we use the representations of the noise currents given in section 2.8 to derive some statistical properties of I(t). The first six sections are concerned with the probability distribution of I(t) and of its zeros and maxima. Sections 3.7 and 3.8 are concerned with the statistical properties of the envelope of I(t). Fluctuations of integrals involving I2(t) are discussed in section 3.9. The probability distribution of a sine wave plus a noise current is given in 3.10 and in 3.11 an alternative method of deriving the results of Part III is mentioned. Prof. Uhlenbeck has pointed out that much of the material in this Part is closely connected with the theory of Markoff processes. Also S. Chandrasekhar has written a review of a class of physical problems which is related, in a general way, to the present subject.22
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)....
[...]