A flattest constrained envelope approach for empirical mode decomposition

PLoS One. 2013 Apr 23;8(4):e61739. doi: 10.1371/journal.pone.0061739. Print 2013.

Abstract

Empirical mode decomposition (EMD) is an adaptive method for nonlinear, non-stationary signal analysis. However, the upper and lower envelopes fitted by cubic spline interpolation (CSI) may often occur overshoots. In this paper, a new envelope fitting method based on the flattest constrained interpolation is proposed. The proposed method effectively integrates the difference between extremes into the cost function, and applies a chaos particle swarm optimization method to optimize the derivatives of the interpolation nodes. The proposed method was tested on three different types of data: ascertain signal, random signals and real electrocardiogram signals. The experimental results show that: (1) The proposed flattest envelope effectively solves the overshoots caused by CSI method and the artificial bends caused by piecewise parabola interpolation (PPI) method. (2) The index of orthogonality of the intrinsic mode functions (IMFs) based on the proposed method is 0.04054, 0.02222 ± 0.01468 and 0.04013 ± 0.03953 for the ascertain signal, random signals and electrocardiogram signals, respectively, which is lower than the CSI method and the PPI method, and means the IMFs are more orthogonal. (3) The index of energy conversation of the IMFs based on the proposed method is 0.96193, 0.93501 ± 0.03290 and 0.93041 ± 0.00429 for the ascertain signal, random signals and electrocardiogram signals, respectively, which is closer to 1 than the other two methods and indicates the total energy deviation amongst the components is smaller. (4) The comparisons of the Hilbert spectrums show that the proposed method overcomes the mode mixing problems very well, and make the instantaneous frequency more physically meaningful.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms*
  • Arrhythmias, Cardiac / diagnosis*
  • Arrhythmias, Cardiac / pathology
  • Databases, Factual
  • Electrocardiography / statistics & numerical data*
  • Humans
  • Nonlinear Dynamics
  • Signal Processing, Computer-Assisted*
  • Signal-To-Noise Ratio

Grants and funding

This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 61101217 and in part by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China under Grant 11KJD510005. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.