Hilbert-Huang Transform And Wavelet Methods For Time-frequency Analysis

For non-stationary signal analysis, it is expected that a desired time-frequency tool should have good resolution in both time and frequency domain so that the variation of frequency components with time could be determined. The recent data-driven tool, Hilbert-Huang transform (HHT), provides a suitable method for time-frequency analysis with adaptive frequency resolution, yet suffers from some unsolved deficiencies.This study gives the numerical analysis of how Empirical Mode Decomposition method—which is the core technology of the HHT method—performs in the separation of multi-component signals and discusses the resolution properties of HHT. On the understanding of the limitedness of HHT, our research combines several technologies to ameliorate the deficiencies such as mode mixing and undesirable pseudo-component problem. By seeking help from the Maximal Overlap Discrete Wavelet Packet Transform (MODWPT), the disjoint dyadic decomposition method and a simple but effective screening process for Intrinsic Mode Function (IMF) selection, a comprehensive improved HHT is put forward. Several experimental study cases will be used to validate the capabilities of the improved HHT. Meanwhile, the efficiency and limitation of this algorithm under different situations is discussed.In addition, this paper introduces the Wavelet Instantaneous Frequency Spectrum which is constructed through identifying the wavelet ridge from wavelet scalogram. Comparative experiments demonstrate that this wavelet-based instantaneous frequency analysis tool offers more precise and crisp time-frequency description of non-stationary multi-component signals than HHT does. This finding may help to eliminate the doubt of wavelet's suitability for time-frequency analysis.