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EEMD signal processing method based on analysis and implementation

In Electronic Infomation Category: E | on April 15,2011

Signal processing, frequency is the signal that the most important. The traditional Fourier transform method does not analyze the frequency of a signal moment in what appears, this resulted in time and WJLXT971ALC.A4 datasheet and frequency simultaneously in the density and WJLXT971ALC.A4 price and intensity of the signal on the time-frequency analysis, such as short time Fourier transform and WJLXT971ALC.A4 suppliers and wavelet transform, but the basic idea of Fourier analysis are based on theory, analysis of nonlinear and nonstationary signals lack of capacity, limited by Heisenberg Uncertainty Principle. HHT (Hilbert Huang Transform) is NEHuang et al in 1998 proposed a new method of time-frequency analysis, to the nonlinear non-stationary signal analysis, also has good adaptability features. Its essence is a smooth signal processing, will have different time scales of the signal level by level to be unbundled.

HHT method in various fields has been widely used, but still has some disadvantages, such as weight and easy to produce false mode mixing and so on. Traditional empirical model (Empirical Mode Decomposit iON, EMD) caused by the decomposition method aliasing modes, France Flandrin EMD algorithm research team led by Huangs own research team and by EMD decomposition of the statistical properties of white noise, the results of numerous studies put forward by adding noise assisted analysis (NA DA) of the EEMD (EnsembleEmpirical Mode Decomposition) method to add white noise signal to add a few missing scales, in the signal decomposition with good performance.

EEMD simulation system using the Matlab platform, GUI controls for system design, can easily be compared visually analyzed to verify the anti-aliasing EEMD in terms of improvement over previous methods.

1 Empirical Mode Decomposition (EMD) and the IMF

HHT method consists of two main steps:

(1) of the original data empirical mode decomposition (EMD), the data decomposition of Hilbert transform to meet the requirements of the n-order intrinsic mode function (IMF) and the residual function of and.

(2) of the Hilbert transform of each IMF order to obtain the instantaneous frequency, and thus obtain the time-frequency map.

Function must be locally symmetric about the timeline, and its been the same number of zeros and extreme points. Such functions are called intrinsic mode function (Int rinsicMode Function, IMF).

EMD method can non-stationary and nonlinear signal decomposition into a set of steady-state and linear sequence set, which is the intrinsic mode function. According to Huangs definition, every step of the IMF should meet two conditions:

(1) data on extreme points and had zero alternately, and an equal number or a maximum difference of any point;

(2) at any point, there is a local maximum and local minimum envelope defined by the mean must be zero.

The selection algorithm is as follows:

(1) For the input signal x (t), to determine x (t) of all extreme points.

(2) cubic spline function with maximum points and minimum points are obtained by fitting x (t) of the upper and lower envelope.

(3) up and down with the original data sequence minus the mean of the envelope.

Average curve:

Detail signal:

(4) usually s (t) does not meet IMF conditions, need to repeat the above steps, the iterative processing, H uang given iteration stop criteria:

SD is the screening threshold, the general value for the 0.2 ~ 0.3, if the calculation of SD is less than this threshold, the filter will be the end of iteration.

After n iterations to meet the stopping criteria obtained by sn (t) is the effective IMF, the remaining signal is entering the next round of selection process.

After several screening, the original data sequence is decomposed into a set of IMF components and a residual, obtained by IMF are stationary, the results obtained by Hilbert transform analysis can be very nonlinear and nonstationary signals .

2 conventional EMD deficiencies and defects

Time scale when the signal changes there jumping on the EMD signal decomposition, there will be a different time scale of IMF components contain characteristic components of the case, called the mode mixing.

The emergence of mode mixing algorithm of EMD on the one hand and the other, by the characteristics of the original signal frequency.

Huang have proposed a detection method to solve the interrupt mode mixing phenomenon, that direct observation of the results, if there is aliasing is re-decomposition, this method requires human posterior judgments.

Chongqing University Tanshan Wen proposed a multi-resolution EMD thinking on a scale provided for each IMF to address the scope of mode mixing, but this method at the expense of EMD good adaptability.

3 into normal white noise EEMD

Order to solve the problem of mode mixing, Huang proposed EEMD, this is a secondary signal processing noise.

Noise reduction technology is designed to remove noise from the signal, but in some cases, the method by adding noise to the secondary analysis, this method is called noise auxiliary clock signal processing (NADA), auxiliary noise signal processing is the most common pre-whitening. White noise added to the signal to smooth the pulse interference, signal analysis is widely used in various fields.

In the EMD method, the IMFs ability to get a reasonable signal depends on the distribution of extreme points, extreme points if the uneven distribution of the signal, there will be the case of mode mixing. To this end, Huang will be decomposed by adding white noise signal, the use of uniform white noise spectrum, when the signal is applied to the spatial distribution throughout the same time-frequency white noise background, the different time scales of the signal will be automatically distributed to the appropriate reference scale, and the characteristics of the zero mean noise, through a series average of the noise will cancel each other out, you can integrate the results of the mean as the final result.

EEMD steps are as follows:

(1) white noise to the signal to a normal distribution.

(2) will join the white noise of the signal into components of the IMF.

(3) Repeat steps (1), (2), each time adding a new white noise sequence.

(4) integration of the IMF get the mean time as the final result.

EMMD algorithm flow shown in Figure 1.

Figure 1 EEMD algorithm flow chart

4 System Function and simulation analysis

To verify the improvements EEMD method, using Mat lab of the GU I designed a simple and intuitive tools for the simulation system.

Realize this system is the function of the input signal EEMD traditional EMD decomposition and decomposition, can display the signal decomposed IMF components of each mode function and its instantaneous frequency and Hilbert time-frequency spectrum can be characterized.

System interface shown in Figure 2.

Figure 2 Simulation System Interface

Parameter setting functions can be freely set by adding white noise of variance and the number of noise group (range 1 to 500), when the variance is set to 0, the number of noise group is selected as 1, the system functions of traditional EMD decomposition.

EEMD decomposition function to set the signal to join the white noise EEMD decomposition and Hilbert depicts the input signal when the spectrum. Show IMFs function

FIG pop-up form displayed by the signal decomposed components of the IMF and the instantaneous frequency.

Simulation results are as follows:

Ideal first samples of multi-component signal decomposition, the signal was constituted as follows:

Where the normalized frequency is:

EMD decomposition method should contain four frequency components of the signal is decomposed into four frequency information of the IMF contains a single component.

Decomposition shown in Figure 3.

Figure 3, the traditional EMD H ilber t of the ideal signal spectrum

Can see that for the ideal signal without interference, the traditional EMD decomposition method has very good results, clearly the four frequency components in the Hilbert spectrum shows up.

Existence of a group of actual interference interrupt signal decomposition, the results shown in Figure 4 to Figure 6.

Figure 4, the actual signal in time domain graph

Figure 5, the traditional signal decomposition EMD

traditional EM D Figure 6, the signal H ilber t spectral characterization

Can be seen through the spectrum, low frequency components mixed together, it is difficult to distinguish.

EEMD decomposition method for the analysis, joined the group standard deviation of 100 0.2 Gaussian white noise, the results shown in Figure 7, shown in Figure 8. By comparison

Hilbert spectrum can be seen, the decomposition results have been greatly improved.

Figure 7 EEMD signal decomposition

Figure 8 EEMD H ilber t of the signal spectrum characterization

5 Concluding Remarks

EEMD auxiliary signal to noise based on the principle, by adding white noise of small amplitude signals to a balanced, effective solution to the aliasing mode, zero mean Gaussian white noise characteristics, so that the true signal has been retained , EMD analysis of traditional great improvement.

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