Hilbert-Huang Transform And Simulation System Design

Hilbert-Huang transform (HHT) is a new signal processing method for analyzing the non-linear and non-stationary signal. The key of HHT is that any complicated data set can be decomposed into some series of intrinsic mode functions (IMF) using the empirical mode decomposition (EMD) method. Furthermore, the instantaneous frequency of IMF can be solved by Hilbert transform. So, we can construct the Hilbert spectrum. Thus, the signal can be analyzed. Although the HHT is adaptive and efficient, it still has some deficiencies, and they influence the validity of application.Firstly, this paper analyzes and simulates many simulative signals in Matlab platform, and it compares the spectrum among short time Fourier spectrum, wavelet spectrum and Hilbert spectrum of Gauss frequency modulation signal. Experiments prove that although short time Fourier transform applies to a stable signal resolution ratio, it is not a dynamic analysis method, and it cannot sensitively show the signal abrupt change. Wigner-Vile distribution is better in time-frequency than short time Fourier transform. However, its crossed parts severely influence the anslyzing results. The wavelet transform has more flexible characteristic and wider application range, so it makes a progress in local property and adaptivity of time-frequency. The HHT decomposes the data according to the characteristic time series, and it obtains some natural oscillation patterns. Thus, the basis of EMD is adaptive and has high decomposition efficiency. In this paper Numerical Experiments prove that HHT has more advantages in analyzing the non-linear and non-stationary signal.Secondly, this paper discusses illusive component brought by HHT. We use the normalization correlation coefficient to recognize the illusive component, and regards the normalize correlation coefficient between IMF and the original signal as the selection criterion. The normalization correlation coefficient can recognize or exclude the illusive component. Numerical experiments prove that this method has an obvious advantage and reasonability in dealing with the illusive component. Otherwise, wavelet transform is treated as a pre-process tool for the mode confusion. We get a better method in improving HHT by combining wavelet transform with normalization correlation coefficient method. The simulation proves the validity of improvd HHT.Finally, a signal simulation system is studied. The system is designed by GUIDE through exporting controls in GUI. It can be divided into four parts including putting control buttons on GUI window, setting the attributes of GUI control buttons, GUI programming and system function realizing. This system realizes some functions. Firstly, some signal transform methods is accomplished, sunch as HHT, EMD, instantaneous frequency of IMF, the amplitude of IMF, Hilbert spectrum and Hilbert edge spectrum et al. Secondly, the comparison is described in wavelet spectrum and Hilbert spectrum. Thirdly, the comparison is described in detail between Wigner-Vile spectrum and Hilbert spectrum. Fourthly, the comparison is depicted among short-time Fourier transform, short-time Fourier spectrum and Hilbert spectrum can be analyzed. Finally, we anslyze Fourier transform, and draw the concolusion between Fourier spectrum and Hilbert edge spectrum. In a word, the simulation system is studied for Hilbert-Huang transform, wavelet transform, Wigner-Vile distribution, short time Fourier transform and Fourier transform. We can compare the result of all those transforms using software program. Through this software, we can understand Hilbert-Huang transform theory deeply and systemically. Meanwhile the application of HHT is also an unceasingly exploring process.