Hilbert-Huang Transform And Its Application In Signal Processing

In recent years, scientists have developed some new methods to process non-stationary signals, but the results are not satisfied. Therefore, N.E.Huang et al in NASA proposed Hilbert-Huang transform (HHT) in 1998, which is a kind of new time-frequency analysis method for nonlinear and non-stationary signals. The key part of the method is the empirical mode decomposition (EMD) method with which any complicated data set can be decomposed into a finite and often-small number of intrinsic mode functions (IMF) that admit well-behaved Hilbert 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 Hilbert transform, the IMF yields instantaneous frequencies and the amplitude functions. The final presentation of the results is an energy-frequency-time distribution, designated as the Hilbert spectrum.In this method, the main conceptual innovations are the introduction of IMF 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. The contents of this are as follows:First, this thesis studies the basic theory of HHT, and illuminates the mathematical definition of instantaneous frequency and IMF. It presents the basic methodology of EMD, considers a simulation to verify the implementation and demonstrate its advantage, as well as the end effect in EMD and the existent methods in solving the problem.Second, this thesis proposes an EMD based epileptic spike detection method. It extracts the high frequency components related to spikes in EEG signal by EMD method. It detects the spikes by calculating the instantaneous amplitude of the high component with Hilbert transform. The results of experiments show that the method works well.Third, EMD does well in extracting the trend in non-stationary signal. EMD is an adaptive, easily implemental relating to the traditional method. It considers four kinds of classical trends as stimulations to verify the validity of EMD comparing with traditional methods.