TY - JOUR
T1 - The empirical mode decomposition and the Hubert spectrum for nonlinear and non-stationary time series analysis
AU - Huang, Norden E.
AU - Shen, Zheng
AU - Long, Steven R.
AU - Wu, Manli C.
AU - Snin, Hsing H.
AU - Zheng, Quanan
AU - Yen, Nai Chyuan
AU - Tung, Chi Chao
AU - Liu, Henry H.
PY - 1998
Y1 - 1998
N2 - 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
AB - 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
KW - Empirical mode decomposition
KW - Frequency-time spectrum
KW - Hubert spectral analysis
KW - Intrinsic time scale
KW - Non-stationary time series
KW - Nonlinear differential equations
UR - http://www.scopus.com/inward/record.url?scp=5444236478&partnerID=8YFLogxK
U2 - 10.1098/rspa.1998.0193
DO - 10.1098/rspa.1998.0193
M3 - 期刊論文
AN - SCOPUS:5444236478
SN - 1364-5021
VL - 454
SP - 903
EP - 995
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
IS - 1971
ER -