TY - JOUR

T1 - On the filtering properties of the empirical mode decomposition

AU - Wu, Zhaohua

AU - Huang, Norden E.

PY - 2010/10

Y1 - 2010/10

N2 - The empirical mode decomposition (EMD) based time-frequency analysis has been used in many scientific and engineering fields. The mathematical expression of EMD in the time-frequency-energy domain appears to be a generalization of the Fourier transform (FT), which leads to the speculation that the latter may be a special case of the former. On the other hand, the EMD is also known to behave like a dyadic filter bank when used to decompose white noise. These two observations seem to contradict each other. In this paper, we study the filtering properties of EMD, as its sifting number changes. Based on numerical results of the decompositions using EMD of a delta function and white noise, we conjecture that, as the (pre-assigned and fixed) sifting number is changed from a small number to infinity, the EMD corresponds to filter banks with a filtering ratio that changes accordingly from 2 (dyadic) to 1; the filter window does not narrow accordingly, as the sifting number increases. It is also demonstrated that the components of a delta function resulted from EMD with any prescribed sifting number can be rescaled to a single shape, a result similar to that from wavelet decomposition, although the shape changes, as the sifting number changes. These results will lead to further understandings of the relations of EMD to wavelet decomposition and FT.

AB - The empirical mode decomposition (EMD) based time-frequency analysis has been used in many scientific and engineering fields. The mathematical expression of EMD in the time-frequency-energy domain appears to be a generalization of the Fourier transform (FT), which leads to the speculation that the latter may be a special case of the former. On the other hand, the EMD is also known to behave like a dyadic filter bank when used to decompose white noise. These two observations seem to contradict each other. In this paper, we study the filtering properties of EMD, as its sifting number changes. Based on numerical results of the decompositions using EMD of a delta function and white noise, we conjecture that, as the (pre-assigned and fixed) sifting number is changed from a small number to infinity, the EMD corresponds to filter banks with a filtering ratio that changes accordingly from 2 (dyadic) to 1; the filter window does not narrow accordingly, as the sifting number increases. It is also demonstrated that the components of a delta function resulted from EMD with any prescribed sifting number can be rescaled to a single shape, a result similar to that from wavelet decomposition, although the shape changes, as the sifting number changes. These results will lead to further understandings of the relations of EMD to wavelet decomposition and FT.

KW - empirical mode decomposition

KW - ensemble empirical mode decomposition

KW - filter banks

KW - Fourier transform

KW - intrinsic mode function

KW - sifting process

KW - sifting stoppage criteria

KW - Time-frequency analysis

KW - wavelet decomposition

UR - http://www.scopus.com/inward/record.url?scp=80052082724&partnerID=8YFLogxK

U2 - 10.1142/S1793536910000604

DO - 10.1142/S1793536910000604

M3 - 期刊論文

AN - SCOPUS:80052082724

SN - 1793-5369

VL - 2

SP - 397

EP - 414

JO - Advances in Adaptive Data Analysis

JF - Advances in Adaptive Data Analysis

IS - 4

ER -