Hilbert-Huang变换及其滤波特性研究

A study of Hilbert-Huang transform and its filtering character

Hilbert-Huang变换是最新发展起来的处理非线性非平稳信号的时频分析方法。其基本的实现分为两步,经验模态分解和瞬时频率的求解。这种方法的核心部分是经验模态分解,任何复杂的信号都可以分解为有限数目并且具有一定物理意义的本征模态函数,对这些本征模态函数作Hilbert变换即可得到每一个本征模态函数的瞬时频率。经验模态分解方法是一个以信号极值特征尺度为度量的时空滤波过程,它充分保留了信号的局部特征,在信号的滤波和去噪中具有较大的优势。本文讨论了Hilbert-Huang变换时空滤波的实现过程,仿真验证了该方法的优越性。

Hilbert-Huang Transform （HHT） is a new two-step time frequency analytic method to analyze the non-linear and non-stationary signal. The key step of this method is empirical mode decomposition （EMD） method with which any complicated data set can be decomposed into several Intrinsic Mode Function （IMF） components. Using Hilbert transform to those IMF components can yield instantaneous frequency. The empirical mode decomposition （EMD） can be interpreted as a temporal and spatial filtering based on the signal＇s extremum characteristic scale. This method preserves the nonlinearity and non-stability of signal, and has potential superiority in filtering and de-noising. The experimental results clarify the advance and efficient of this method.