An Analytical Expression for Empirical Mode Decomposition Based on B-Spline Interpolation

2013 ◽  
Vol 32 (6) ◽  
pp. 2899-2914 ◽  
Author(s):  
Yanli Yang ◽  
Changyun Miao ◽  
Jiahao Deng
Keyword(s):  
Empirical Mode Decomposition ◽  
Spline Interpolation ◽  
B Spline ◽  
Analytical Expression ◽  
Mode Decomposition

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.

Two-dimensional empirical mode decomposition by finite elements

2006 ◽  
Vol 462 (2074) ◽  
pp. 3081-3096 ◽  
Author(s):  
Y Xu ◽  
B Liu ◽  
J Liu ◽  
S Riemenschneider
Keyword(s):  
Finite Element ◽  
Linear Combination ◽  
Empirical Mode Decomposition ◽  
Spline Interpolation ◽  
Basis Functions ◽  
Two Dimensional ◽  
Element Analysis ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Mode Decomposition

Empirical mode decomposition (EMD) is a powerful tool for analysis of non-stationary and nonlinear signals, and has drawn significant attention in various engineering application areas. This paper presents a finite element-based EMD method for two-dimensional data analysis. Specifically, we represent the local mean surface of the data, a key step in EMD, as a linear combination of a set of two-dimensional linear basis functions smoothed with bi-cubic spline interpolation. The coefficients of the basis functions in the linear combination are obtained from the local extrema of the data using a generalized low-pass filter. By taking advantage of the principle of finite-element analysis, we develop a fast algorithm for implementation of the EMD. The proposed method provides an effective approach to overcome several challenging difficulties in extending the original one-dimensional EMD to the two-dimensional EMD. Numerical experiments using both simulated and practical texture images show that the proposed method works well.

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.

A REINTERPRETATION OF EMD BY CUBIC SPLINE INTERPOLATION

2011 ◽  
Vol 03 (04) ◽  
pp. 527-540 ◽  
Author(s):  
MINJEONG PARK ◽  
DONGHOH KIM ◽  
HEE-SEOK OH
Keyword(s):  
Empirical Mode Decomposition ◽  
Time Domain ◽  
Spline Interpolation ◽  
Cubic Spline ◽  
Data Driven ◽  
Constant Frequency ◽  
Cubic Spline Interpolation ◽  
Mode Decomposition ◽  
The Time Domain ◽  
Theoretical Results

Empirical mode decomposition (EMD) is a data-driven technique that decomposes a signal into several zero-mean oscillatory waveforms according to the levels of oscillation. Most of the studies on EMD have focused on its use as an empirical tool. Recently, Rilling and Flandrin, [2008] studied theoretical aspects of EMD with extensive simulations, which allow a better understanding of the method. However, their theoretical results have been obtained by considering constraints on the signal such as equally spaced extrema and constant frequency. The present study investigates the theoretical properties of EMD using cubic spline interpolation under more general conditions on the signal. This study also theoretically supports modified EMD procedures in Kopsinis and Mclaughlin, [2008] and developed for improving the conventional EMD. Furthermore, all analyses are preformed in the time domain where EMD actually operates; therefore, the principle of EMD can be visually and directly captured, which is useful in interpreting EMD as a detection procedure of hidden components.

scholarly journals Reducing the residual error of multibeam sounding data through empirical mode decomposition based on cubic Bessel interpolation

2021 ◽  
Vol 15 ◽  
pp. 174830262110083
Author(s):  
Jialong Sun ◽  
Zhengyang Zhang ◽  
Chi Zhang ◽  
Jinlei Liu ◽  
Peng Zhang
Keyword(s):  
Empirical Mode Decomposition ◽  
Spline Interpolation ◽  
Residual Error ◽  
Improved Method ◽  
Depth Data ◽  
Mode Decomposition ◽  
The Mean ◽  
Residual Errors ◽  
Original Water ◽  
Echo Sounding

The systematic residual errors present in multibeam echo-sounding data cause the areas of overlap between adjacent swaths to become distorted. A method is proposed in this paper to reduce the residual error of multibeam sounding data through empirical mode decomposition (EMD) based on cubic Bessel interpolation. Numerical experiments confirm that the discrepancy in the overlap between two swaths is significantly reduced after applying EMD improved by cubic Bessel interpolation compared with both the original water depth data and with data processed using conventional EMD based on cubic spline interpolation. The mean square error of the improved method is decreased by 67% and 29% compared with that of the original and conventional EMD cases, respectively. Therefore, EMD with cubic Bessel interpolation can efficiently reduce the residual error of multibeam echo-sounding data.

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