联合采用高通低通滤波与Hilbert-黄变换的非线性信号分析

经验模态分解方法无法分离2倍频内信号分量而可能导致模态混叠,这是应用著名的Hilbert-黄变换(Hilbert-Huang Transform,HHT)分析非线性信号时无法回避的问题,而消除模态混叠对于准确分析非线性信号具有重要意义。在此背景下,提出了一种联合采用高通低通滤波与Hilbert-黄变换的非线性信号分析方法,以解决这一问题。首先,提出了基于HHT瞬时频率的、用于判断是否发生模态混叠的指标;在此基础上为解决常规经验模态分析方法无法分解2倍频内信号的问题,采用傅里叶变换分析存在模态混叠的信号,并通过高通低通滤波将2倍频内的信号分离。之后,对经过滤波后的信号进行经验模态分解,并与之前未发生模态混叠的分量整合,得到原始信号完整的本征模态函数分量,进而计算得到各分量的瞬时频率和瞬时幅值。最后,用算例说明了所提方法的基本特征。

Combined use of high-pass and low-pass filtering as well as hilbert-huang transform for nonlinear signal analysis

The mode mixing problem in the empirical mode decomposition(EMD) is ineluctable when employing the well-known Hilbert-Huang Transform(HHT) to analyze nonlinear signals,and hence it is essential to solve this problem for achieving accurate signal analysis.Given this background,a method is proposed to solve this problem by the combined use of high-pass and low-pass filtering as well as the Hilbert-Huang transform for nonlinear signal analysis.An index is proposed to identify whether the mode mixing exists by analyzing the instantaneous frequency of HHT.In order to solve the mode mixing problem that may be caused by directly applying the EMD,the Fourier transform is employed to identify the signal components caused the mode mixing,and the high-pass and low-pass filtering to separate the signal components within the same octave.Then,the EMD is used to decompose the filtered signal,and the complete intrinsic mode functions(IMFs) are obtained by integrating the IMFs with the signal components without mode mixing.The instantaneous frequency and amplitude of the IMFs are next obtained.Finally,a sample example is served for demonstrating the feasibility of the proposed method.