BOUNDARY EXTENSION AND STOP CRITERIA FOR EMPIRICAL MODE DECOMPOSITION

2010 ◽  
Vol 02 (02) ◽  
pp. 157-169 ◽  
Author(s):  
QIN WU ◽  
SHERMAN D. RIEMENSCHNEIDER
Keyword(s):  
Empirical Mode Decomposition ◽  
Numerical Experiments ◽  
Boundary Extension ◽  
B Spline ◽  
Mode Decomposition ◽  
Mirror Extension

In this paper, a new idea about the boundary extension has been introduced and applied to the Empirical Mode Decomposition (EMD) algorithm. Instead of the traditional mirror extension on the boundary, we propose a ratio extension on the boundary. We also adopt the stop criteria by Rilling et al. for B-Spline based EMD algorithm. Numerical experiments are used for empirically assessing performance of the modified EMD algorithm. The examples indicate that the ratio boundary extension indeed improves the result of the original EMD.

B-SPLINE ANALYTICAL REPRESENTATION OF THE MEAN ENVELOPE FOR EMPIRICAL MODE DECOMPOSITION

2010 ◽  
Vol 08 (02) ◽  
pp. 175-195 ◽  
Author(s):  
TIANXIANG ZHENG ◽  
LIHUA YANG
Keyword(s):  
Empirical Mode Decomposition ◽  
Basic Concept ◽  
Spline Functions ◽  
Mathematical Foundation ◽  
Knot Insertion ◽  
B Spline ◽  
Explicit Formulation ◽  
Novel Approach ◽  
Mode Decomposition ◽  
The Mean

This paper investigates how the mean envelope, the subtrahend in the sifting procedure for the Empirical Mode Decomposition (EMD) algorithm, represents as an expansion in terms of basis. To this end, a novel approach that gives an alternative analytical expression using B-spline functions is presented. The basic concept lies mainly on the idea that B-spline functions form a basis for the space of splines and have refined-node representations by knot insertion. This newly-developed expression is essentially equivalent to the conventional one, but gives a more explicit formulation on this issue. For the purpose of establishing the mathematical foundation of the EMD methodology, this study may afford a favorable opportunity in this direction.

scholarly journals An Improved EMD and Its Applications to Find the Basis Functions of EMI Signals

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Hongyi Li ◽  
Chaojie Wang ◽  
Di Zhao
Keyword(s):  
Empirical Mode Decomposition ◽  
Spline Interpolation ◽  
Basis Functions ◽  
B Spline ◽  
Minimal Points ◽  
Mode Decomposition ◽  
Lower Envelopes ◽  
The Mean ◽  
The Cost ◽  
Emd Method

A B-spline empirical mode decomposition (BEMD) method is proposed to improve the celebrated empirical mode decomposition (EMD) method. The improvement of BEMD on EMD mainly concentrates on the sifting process. First, instead of the curve that resulted from computing the average of upper and lower envelopes, the curve interpolated by the midpoints of local maximal and minimal points is used as the mean curve, which can reduce the cost of computation. Second, the cubic spline interpolation is replaced with cubic B-spline interpolation on account of the advantages of B-spline over polynomial spline. The effectiveness of BEMD compared with EMD is validated by numerical simulations and an application to find the basis functions of EMI signals.

A CRITERION FOR SELECTING RELEVANT INTRINSIC MODE FUNCTIONS IN EMPIRICAL MODE DECOMPOSITION

2010 ◽  
Vol 02 (01) ◽  
pp. 1-24 ◽  
Author(s):  
ALBERT AYENU-PRAH ◽  
NII ATTOH-OKINE
Keyword(s):  
Empirical Mode Decomposition ◽  
Numerical Experiments ◽  
Numerical Procedure ◽  
Basis Functions ◽  
Natural Phenomena ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Numerical Errors ◽  
Mode Decomposition ◽  
Study Results

Information extraction from time series has traditionally been done with Fourier analysis, which use stationary sines and cosines as basis functions. However, data that come from most natural phenomena are mostly nonstationary. A totally adaptive alternative method has been developed called the Hilbert–Huang transform (HHT), which involves generating basis functions called the intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD). The EMD is a numerical procedure that is prone to numerical errors that may persist in the decomposition as extra IMFs. In this study, results of numerical experiments are presented, which would establish a stringent threshold by which relevant IMFs are distinguished from IMFs that may have been generated by numerical errors. The threshold is dependent on the correlation coefficient between the IMFs and the original signal. Finally, the threshold is applied to IMFs of earthquake signals from five accelerometers located in a building.

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