Empirical mode decomposition and the hilbert-huang transform

This chapter discusses the empirical mode decomposition (EMD) and the bidimensional empirical mode decomposition (BEMD) as well as theHilbert-Huang transformmethod (HHT). TheHHT combines the EMD and the Hilbert spectral analysis; the Hilbert spectral analysis involves the Hilbert transform of the basis functions generated by the EMD. The HHT has been developed to handle nonstationary data, which are properties of almost all physical processes that are sampled for analysis. Traditionally, Fourier-based approaches have been the main analysis procedures for such physical processes, but stationarity must be assumed for Fourier-based methods. The HHT, by the nature of the method, presents a relative advantage over the Fourier analysis methods because it does not implicitly assume stationarity. The EMD has been extended to handle 2-D data, such as images, using the BEMD, which follows a similar procedure as the 1-D version. Huang et al. (1998) introduced the HHT as a signal-processing tool that adaptively decomposes nonstationary signals into basis functions called intrinsic mode functions (IMF). The Hilbert transform of each IMF is well behaved, and the instantaneous frequency and instantaneous amplitude can be determined from the subsequent analytic signal that is formed from the IMF and its Hilbert transform. The instantaneous frequency and instantaneous amplitude may be used to plot an energy-frequency-time spectrum of the original signal.