Noise Corruption of Empirical Mode Decomposition and its Effect on Instantaneous Frequency

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal's instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be nearly monochromatic, a condition that is not guaranteed by the algorithm and fails to be met when the signal is corrupted by noise. In this work, the extraction of modes containing both signal and noise is identified as the cause of poor IF estimation. The specific mechanism by which such "transition" modes are extracted is detailed and builds on the observation of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing pure noise. The mechanism is shown to be dependent on spectral leak between modes and the phase of the underlying signal. These ideas are developed through the use of simple signals and are tested on a synthetic seismic waveform.

[1]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[2]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  David R. Brillinger,et al.  Time Series: Data Analysis and Theory. , 1982 .

[4]  Norden E. Huang,et al.  HHT-BASED BRIDGE STRUCTURAL HEALTH-MONITORING METHOD , 2005 .

[5]  Philippe Gaillot,et al.  Characterization of seismic waveforms and classification of seismic events using chirplet atomic decomposition. Example from the Lacq gas field (Western Pyrenees, France) , 2006 .

[6]  Norden E. Huang,et al.  Ensemble Empirical Mode Decomposition: a Noise-Assisted Data Analysis Method , 2009, Adv. Data Sci. Adapt. Anal..

[7]  A. Walden,et al.  The Hilbert spectrum via wavelet projections , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[8]  Boualem Boashash,et al.  Estimating and interpreting the instantaneous frequency of a signal. II. A/lgorithms and applications , 1992, Proc. IEEE.

[9]  Patrick J. Loughlin,et al.  Instantaneous frequency and the conditional mean frequency of a signal , 1997, Signal Process..

[10]  Paulo Gonçalves,et al.  Empirical Mode Decompositions as Data-Driven Wavelet-like Expansions , 2004, Int. J. Wavelets Multiresolution Inf. Process..

[11]  Norden E. Huang,et al.  On Instantaneous Frequency , 2009, Adv. Data Sci. Adapt. Anal..

[12]  Ahsan Kareem,et al.  Performance of Wavelet Transform and Empirical Mode Decomposition in Extracting Signals Embedded in Noise , 2007 .