Hilbert-Huang变换的自适应频率多分辨分析研究

Study of Adaptive Frequency Multiresolution Analysis of the Hilbert-Huang Trans form

Hilbert -Huang变换方法能自适应地提取非平稳数据的局部均值曲线 ,将复杂的叠加信号分解成有限数量的、且有物理意义的内蕴模式分量函数 ,从而得到有意义的瞬时频率和希尔伯特时频谱 .它是一种局域波分析方法 .其特点是比小波分析有更高的时频分辨率 ,没有Wigner- Ville分布的交叉项 ,特别适合分析非平稳数据 .本文根据Hilbert- Huang变换的原理 ,推导出内蕴模式函数的递推表达式 ,给出了希尔伯特谱的最高频率分辨率 ,首次提出了一种新的的自适应频率多分辨分析原理和方法 ,从而完善了局域波分析的理论 .

Through extracting the local mean value curve of nonlinear and non-stationary data, any complicated data set can be adaptively decomposed into a finite number of Intrinsic Mode Functions (IMFs) which have physical meaning and can be expressed in a kind of joint energy-frequency-time distribution form by the HHT (Hilbert-Huang Transform), a typical realization of the Local Wave Analysis (LWA), so a meaningful instantaneous frequency can be obtained. The method has some good features compared to the other methods, such as having better joint time-frequency resolution than Wavelet analysis, and without cross terms that exist in Wigner-Ville distribution analysis. Therefore, it is especially powerful for analysis of non-stationary and nonlinear signals. In this paper, the mathematic expressions of IMFs and the limit of frequency resolution of the HHT are discussed further, and a new principle and method of adaptive frequency multiresolution analysis is put forward for developing the theory of the LWA.