Research on Hilbert-Huang transform
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Nonlinear and non-stationary signal processing has been always a hot issue.Hilbert-Huang transform is a new signal processing method,which can get the time-frequency-energy distribution characteristics of the signals through the empirical mode decomposition(EMD) and Hilbert transform.But when it is in application,the results gained are not very precise,some improvements are proposed,and it proved feasibility and useful through MATLAB simulation.Keywords:
Hilbert spectral analysis
SIGNAL (programming language)
Instantaneous phase
S transform
Energy distribution
Mode (computer interface)
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In order to analyze the dynamic response of linear 2-DOF system and identify the influence of all the factors on it,a new time-frequency method named Hilbert-Huang transform was applied in the time-frequency analysis of linear 2-DOF system,which was put forward by Norden E.Huang in USA.The dynamic response was decomposed into significant IMF by Empirical Mode Decomposition.After performing the Hilbert transform,the IMFs can achieve the Hilbert spectra.It clearly shows the action of the natural frequency and prompting frequency.The Hilbert-Huang Transform does better than Fourier Transform in the time domain,which can show the dynamic character in time-frequency domain.The method is accurate and valid in the time-frequency analysis.
Hilbert spectral analysis
Instantaneous phase
Constant Q transform
S transform
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The Hilbert-Huang transform is more suitable methods for analysing non-stationary data.It has been developed by Norden E. Huang and others. This method is the seedtime, and there are many unbeknown factors in developing exact theoretics. In this paper, firstly, the author introduce the Hilbert -Huang transform. Secondly, contraposing the problems that exist in the original arithmetic, the author put forward a modified method. Finally, the author contrasts the modified method and the original method, and demonstrates that using the modified method, people could gain more precisely IMFs which kept the character of instantaneous frequency of original signal’s components.
Instantaneous phase
SIGNAL (programming language)
Hilbert spectral analysis
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The Empirical Mode Decomposition (EMD) is a new adaptive signal decomposition method, which is good at handling many real nonlinear and nonstationary one dimensional signals. It decomposes signals into a a series of Intrinsic Mode Functions (IMFs) that was shown having better behaved instantaneous frequencies via Hilbert transform (The EMD and Hubert spectrum analysis together were called Hilbert-Huang Transform (HHT) which was proposed by N.E. Huang et al, in.). For the advanced applications in image analysis, the EMD was extended to the bidimensional EMD (BEMD). However, most of the existed BEMD algorithms are slow and have unsatisfied results. In this paper, we firstly proposed a new BEMD algorithm which is comparatively faster and better-performed. Then we use the Riesz transform to get the monogenic signals. The local features (amplitude, phase orientation, phase angle, etc) are evaluated. The simulation results are given in the experiments.
Instantaneous phase
Hilbert spectral analysis
Mode (computer interface)
SIGNAL (programming language)
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According to the mode mixing problem caused by empirical mode decomposition(EMD),the Hilbert-Huang transform based on Ensemble Empirical Mode Decomposition(EEMD) is introduced into fault signal detection of power system,it can overcome the mode mixing problem in?a great extent,and ensure the physical meaning of signal components.The signal is firstly decomposed into intrinsic mode function(IMF) by the EEMD method,then Hilbert spectrum is obtained form Hilbert transform.The transient and disturbances can be analyzed and detected accurately through the Hilbert spectrum.Simulation results show that the method can be applied to fault signal detection of power system effectively.
SIGNAL (programming language)
Transient (computer programming)
Mode (computer interface)
Empirical orthogonal functions
Hilbert spectral analysis
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An economic signal in the real world usually reflects complex phenomena. One may have difficulty both extracting and interpreting information embedded in such a signal. A natural way to reduce complexity is to decompose the original signal into several simple components, and then analyze each component. Spectral analysis (Priestley, 1981) provides a tool to analyze such signals under the assumption that the time series is stationary. However when the signal is subject to non-stationary and nonlinear characteristics such as amplitude and frequency modulation along time scale, spectral analysis is not suitable. Huang et al. (1998b, 1999) proposed a data-adaptive decomposition method called empirical mode decomposition and then applied Hilbert spectral analysis to decomposed signals called intrinsic mode function. Huang et al. (1998b, 1999) named this two step procedure the Hilbert-Huang transform(HHT). Because of its robustness in the presence of nonlinearity and non-stationarity, HHT has been used in various fields. In this paper, we discuss the applications of the HHT and demonstrate its promising potential for non-stationary financial time series data provided through a Korean stock price index.
Hilbert spectral analysis
Stationary process
Singular Spectrum Analysis
Instantaneous phase
Robustness
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Empirical mode decomposition is a novel approach for processing signal,which overcomed the drawback of Fourier transform and wavelet transform and can adaptively process the norlinear and non-stationary signal,so this approach has been used in many fields.On the basis of analyzing the shortcoming of Fourier transform and wavelet transform,the article in details sets out the theatical basis,method and the frontier research issues of the empirical mode decomposition.
Harmonic wavelet transform
Constant Q transform
S transform
SIGNAL (programming language)
Basis (linear algebra)
Second-generation wavelet transform
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The selection of different basis functions with the methods such as Fourier transform and wavelet transform will lead to different results in the decomposition of dynamic measurement error.Hilbert-Huang transform(HHT) for dynamic measurement error decomposition is proposed in this paper.The method does not need to select the basis function and can decompose the dynamic measurement error signal adaptively.The error model of whole system was established for a hybrid dynamic measurement system.The total errors of the measurement system were analyzed with Hilbert-Huang transform.The result of Hilbert-Huang transform decomposition is more accurate than Fourier transform and wavelet transform decomposition results and is consistent with the measurement error model.
Harmonic wavelet transform
Hilbert spectral analysis
Constant Q transform
Hartley transform
Basis (linear algebra)
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Empirical Mode Decomposition (EMD) is a data-driven technique for extraction of oscillatory components from data. Although it has been introduced over 15 years ago, its mathematical foundations are still missing which also implies lack of objective metrics for decomposed set evaluation. Most common technique for assessing results of EMD is their visual inspection, which is very subjective. This article provides objective measures for assessing EMD results based on the original definition of oscillatory components.
Mode (computer interface)
Empirical Research
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Hilbert spectral analysis
Instantaneous phase
S transform
SIGNAL (programming language)
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The well-known Hilbert–Huang transform (HHT) consists of empirical mode decomposition to extract intrinsic mode functions (IMFs) and Hilbert spectral analysis to obtain time–frequency characteristics of IMFs through the Hilbert transform. There are two mathematical requirements that limit application of the Hilbert transform. Moreover, noise effects caused by the empirical mode decomposition procedure add a scatter to derivative-based instantaneous frequency determined by the Hilbert transform. In this paper, a new enhanced HHT is proposed in which by avoiding mathematical limitations of the Hilbert spectral analysis, an additional parameter is employed to reduce the noise effects on the instantaneous frequencies of IMFs. To demonstrate the efficacy of the proposed method, two case studies associated with structural modal identification are selected. In the first case, through identification of a typical 3-DOF structural model subjected to a random excitation, accuracy of the enhanced method is verified. In the second case, ambient response data recorded from a real 15-story building are analyzed, and nine modal frequencies of the building are identified. The case studies indicate that the enhanced HHT provides more accurate and physically meaningful results than HHT and is capable to be an efficient tool in structural engineering applications. Copyright © 2012 John Wiley & Sons, Ltd.
Hilbert spectral analysis
Instantaneous phase
Mode (computer interface)
Identification
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