The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis

Norden E. Huang, Zheng Shen, Steven R. Long, Manli C. Wu, Hsing H. Snin, Quanan Zheng, Nai Chyuan Yen, Chi Chao Tung, Henry H. Liu

Research output: Contribution to journalArticlepeer-review

22732 Scopus citations

Abstract

A new method for analysing nonlinear and non-stationary data has been developed. The key part of the method is the 'empirical mode decomposition' method with which any complicated data set can be decomposed into a finite and often small number of 'intrinsic mode functions' that admit well-behaved Hubert transforms. This decomposition method is adaptive, and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. With the Hubert transform, the 'instrinic mode functions' yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy-frequency-time distribution, designated as the Hubert spectrum. In this method, the main conceptual innovations are the introduction of 'intrinsic mode functions' based on local properties of the signal, which makes the instantaneous frequency meaningful; and the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need for spurious harmonics to represent nonlinear and non-stationary signals. Examples from the numerical results of the classical nonlinear equation systems and data representing natural phenomena are given to demonstrate the power of this new method. Classical nonlinear system data, are especially interesting, for they serve to illustrate the roles played by the nonlinear and non-stationary effects in the energy-frequency-time distribution

Original languageEnglish
Pages (from-to)903-995
Number of pages93
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume454
Issue number1971
DOIs
StatePublished - 1998

Keywords

  • Empirical mode decomposition
  • Frequency-time spectrum
  • Hubert spectral analysis
  • Intrinsic time scale
  • Non-stationary time series
  • Nonlinear differential equations

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