The Research Of HHT Time-Frequecy Analysis Method And Its Application

Generally, nonlinear signals, non-gaussian and non-stationary signals wereanalyzed and disposed in course of the signal processing. The development ofnon-stationary signal processing was paid attention especially. The traditionalapproaches for analyzing non-stationary signals were the short-time Fouriertransform, the Wigner-Ville distribution and the wavelet analysis and so on. Theshort-time Fourier transform is a method with great efficiency and simpleness, butit's time resolution conflicts with the frequency resolution. We must reduce the timeresolution to increase the frequency resolution and vice versa. It restricts theanalysis precision of STFT. The Wigner-Ville distribution describes the signals withplanar distribution. The difficulty with this method is the severe cross terms asindicated by the existence of negative power for some frequency ranges. Thewavelet approach has been available only in the last ten years or so, but it hasbecome extremely popular. A very appealing feature of the wavelet analysis is thatit provides a adjustable resolution for all the scales. The problem with the method isits linear and non-adaptive nature. It can only give a physically meaningfulinterpretation to linear phenomena. And once the basic wavelet is selected, one willhave to use it to analyze all the data. Essentially these methods is Fourier based,therefore, they suffer the many shortcomings of Fourier spectral analysis.Hilbert-Huang transform is a new technology for the analysis of thenon-stationary signals, which was introduced by N.E.Huang in 1998.This methodconsists of two successive parts: the empirical mode decomposition (EMD)and the Hilbert spectral analysis (HSA).Firstly, an arbitrary non-stationarysignal is decomposed into a number of data sequences, which have differencecharacteristic time scales. The data sequence is known as intrinsic modefunction (IMF). Then, HSA is performed on each decomposed IMF, and theHilbert spectrum of the corresponding IMF is obtained. At last, the Hilbertspectra of all IMFs are grouped to get the energy-frequency-time distributionof the original signal, designated as the Hilbert spectrum. The essence of themethod is to identify the intrinsic oscillatory modes by their characteristictime scales in the data empirically, and then decompose the data accordingly.Ultimately the instantaneous frequency and energy rather than the globalfrequency and energy defined by the Fourier spectral analysis represent thefrequency components of the original signal and eliminate the need forspurious harmonics to represent nonlinear and non-stationary signals inFourier analysis.In HHT method, the cubic spline line is applied to connect the extrema ofsignal as the upper and lower envelopes. The serious problems of the spline fittingcan occur near the ends, where the cubic spline fitting can have large swings. Leftby themselves, the end swings can eventually propagate inward and corrupt thewhole data span especially in the low-frequency components. We can throw awaythe end data to reduce the envelope distortion for the long data series, but it isunreliable for the short data series. This is the HHT's end effects.This paper devises a mended method to eliminate the HHT's end effects. Thesymmetry extending technology and the period extending technology are used toextend the signal series and then the extended signal is decomposed into IMFs byEMD. We can obtain more exact IMFs through throwing away the extended parts ofIMF components. We can also obtain more clear energy-frequency-time distributionthrough applying the HSA to the extended IMFs. In this paper, we use thesymmetry extending technology and the period extending technology to extendrespectively the linear superposition signal of cosine functions and parabolafrequency-modulated signal. The results illuminate the mended method canobliterate the fluctuations of the end data and hold the characteristic time scales ofIMF components perfectly and represent the time-frequency property of the enddata much more clear and exact and control well the influences of HHT's endeffects.HHT method is applied to analyze non-stationary signal, but can it alsoanalyze other signals? We use the mended HHT method to analyze a number ofnonlinear/linear, non-stationary/stationary signals, for example: transient signal,linear frequency-modulated signal and so on. The results illuminate HHT method isadaptive and highly efficient. Since HHT method is based on the local characteristictime scale of the data, it is applicable to nonlinear and non-stationary processes. Butthe results show it is also applicable to linear and stationary processes. HHTmethod can analyze not only mono-component signal but also multi-componentssignal. Comparing HHT method to traditional time-frequency method: short-timeFourier transform, Wigner-Ville distribution and wavelet transform, we canconsider that HHT method is better than the others. HHT method offers very highresolution of time and frequency, which other time-frequency distributions canhardly achieve.Application of HHT method is studied in this paper at last. HHT method isapplied to analyze non-stationary signal interfused the colored noise and radar echosignal. The signals are generally submerged by the noise in the practicalengineering. We can eliminate the noise through abandoning the IMFs with thenoise and integrating the IMFs with signal information. Then HHT method isapplied successfully in radar echo signal processing. It represents thetime-frequency property of radar echo signal clearly and exactly. The resultsilluminate HHT method is a time-frequency analysis method with great efficiencyand it can resume or extract the time-frequency properties of the signal even if inthe background of noise.