Research On The Theory And Application Of Hilbert-huang Transform

As a nonlinear and non-stationary data analysis method, Hilbert-Huang Transform (HHT) consists of Empirical Mode Decomposition (EMD) and Hilbert Spectrum Analysis (HSA). EMD, so-called'sifting'processing, decomposes any complicated raw signal into a finite and often small number of Intrinsic Mode Functions (IMF), which admits well-behaved Hilbert transforms to yield instantaneous frequencies as functions of time. HHT is used to detect the inter-wave signal and intra-wave signal. HHT not only find the hopping point in inter-wave signal, but also detects frequency modulation in the intra-wave signal precisely. Compared with the results of wavelet decomposition and Fourier analysis, the HHT is advantageous.Ensemble empirical mode decomposition (EEMD) is a noise-assisted adaptive data analysis method to solve the problem of mode mixing caused by EMD. However, the ensemble number and amplitude of added noise are two parameters are required to determine before the decomposition processes. A novel fast EEMD preferences algorithm called Quasi-Gradient Search (QGS) is proposed. QGS increases the ensemble number exponentially. For a given ensemble number, we estimate the lower bound of decomposition error, which leads to the best amplitude of added noise. Simulation results demonstrate that QGS is fast, high-efficient and greatly maneuverable. Compared with the result of traditional EEMD, the proposed QGS can greatly enhance the calculation speed with the same decomposition accuracy.In practical application, medical ultrasonic signal is often polluted by'trumpet-shape'noise. In this paper, a denoising method is proposed based on EEMD and nonlinear correlation analysis. We decompose medical ultrasound signal by EEMD, combined with the NCIE as the evaluation criteria to choose the combination of IMFs as filter result and finally accomplish the removal of trumpet type noise. Through simulation experiments, we demonstrate the effectiveness of the method.Nonlinear Correlation Coefficient (NCC) is proposed to quantitatively measure the nonlinear relationship between the variables. In this paper, we develop a mathematical theory about the effects of variables distribution on NCC. We explore that the arbitrary change caused by more chaotic distribution of variables leads to NCC decrease and study that the average sharing structure of the concerned variables minimizes the NCC. Furthermore, we consider the situation of variables'sampling numbers increasing and provide a rigorous proof to a set of mathematical results justifying that NCC is an increasing function as the numbers of sampling points increase. The numerical examples from Lorenz system and linear auto regression system are used to illustrate these theoretical results.