The Research Of Hilbert-Huang Transform Based On Multi-resolution Analysis

Hilbert-Huang transform (HHT) is a new two-step time-frequency analytic method to analyze the nonlinear and the non-stationary signal. The key step of this 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). Using Hilbert transform to those IMF components can yield instantaneous frequency, the final presentation of this results is an energy-frequency-time distribution, designated as the Hilbert spectrum.This paper discussed the definition of instantaneous frequency and it's calculation in continuous and discrete time. Instantaneous frequency is function of time that gives sharp identification of imbedded structures in signal. Obtaining meaningful instantaneous frequency hove to be restricted to the mono-component signal, for multi-component signal, it is necessary to decompose this signal into the combination of some mono-component signals. In this paper, based on the local properties of signal, define a class of function designated as intrinsic mode function i in which the instantaneous frequency can be defined everywhere.The empirical mode decomposition Method is adaptive and highly efficient, meanwhile, this method is time consuming and may run into difficulties when the data contains intermittence which will cause mode mixing. This paper invokes the multi-resolution analytic technology into the EMD, develops the sectional intrinsic mode function and constructs multi-resolution EMD method (MEMD). Using a series of adjustable time windows to control the shifting process can yield a multi-scale decomposition of signal. The MEMD method can notable decrease the time consuming and efficiently overcome the mode mixing. Since this decomposition is based on the local characteristic time scale of the signal, it is applicable to nonlinearrand non-stationary process. Using Hilbert transform to those sectional IMF components can obtain the presentation of signal that represents a generalized Fourier expansion. Furthermore yield the Hilbert spectrum.Combination of the MEMD method and the Hilbert spectrum method sets upvthe multi-resolution Hilbert-Huang transform (MHHT). The MHHT not only provides a more precise definition of particular events in time-frequent space than wavelet analysis, but also provides a more physically meaningful interpretation of the underlying dynamic processes and overcomes the difficult to choose the wavelet in wavelet transform. In this paper, examples from the numerical results of the classical nonlinear equation system and data representing natural phenomena are given to demonstrate the power of this new meshed .those results can clarity the advance and efficient of this method.