Derivative-optimized Empirical Mode Decomposition for the Hilbert-Huang Transform

Abstract

In the Empirical Mode Decomposition (EMD) for the Hilbert-Huang Transform (HHT) a nonlinear and nonstationary signal is adaptively decomposed by HHT into a series of Intrinsic Mode Functions (IMFs) with the lowest one as the trend. At each step of the EMD, the low-frequency component is mainly determined by the average of upper envelope (consisting of local maxima) and lower envelopes (consisting of local minima). The high-frequency component is the deviation of the signal relative to the low-frequency component. The fact that no local maximum and minimum can be determined at the two end-points leads to detrend uncertainty and in turn causes uncertainty in HHT. To reduce such uncertainty, the Hermitian polynomials are used to obtain the upper and lower envelopes with the first derivatives at the two end-points (qL, qR) as parameters, which are optimally determined on the base of minimum temporal variability of the low-frequency component in the each step of the decomposition. This well-posed mathematical system is called the Derivative-optimized EMD (DEMD). With the DEMD the end effect, and detrend uncertainty are drastically reduced, and scales are separated naturally without any a-priori subjective selection criterion.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2013
Accession Number
ADA582395

Entities

People

  • Chenwu Fan
  • Norden Huang
  • Peter Cheng Chu

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Adaptive Filters
  • Algorithms
  • Applied Mathematics
  • Complex Variables
  • Computations
  • Data Analysis
  • Decomposition
  • Equations
  • Frequency
  • Harmonics
  • Information Operations
  • Linear Algebraic Equations
  • Mathematics
  • Polynomials
  • Stationary
  • Time Intervals
  • Time Series Analysis

Readers

  • Linear Algebra
  • Regression Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.