基于奇异谱分析的经验模态分解去噪方法

提出了一种基于奇异谱分析(SSA)的经验模态分解(EMD)去噪方法。该方法先对带噪信号进行EMD分解,得到若干个本征模态函数(IMF)。再通过SSA对每个IMF分量进行去噪处理:把第一个IMF分量作为高频噪声,并根据它计算出剩余IMF中所含的噪声能量,从而得到剩下的每个IMF中信号所占的能量比值。然后选择合适的窗口长度,对每个IMF进行SSA变换,根据IMF中信号所占的能量比值选择合适的奇异值分解(SVD)分量重构,得到去噪后的IMF。再将所有重构得到的IMF分量以及余项相加,得到最终去噪后的信号。经过实验,对比研究了该方法与小波软阈值、EMD软阈值和EMD滤波方法的去噪效果,结果表明该方法整体优于其它方法,是一种有效的信号去噪方法。

An empirical mode decomposition de-noising method based on singular spectrum analysis

We propose an empirical mode decomposition (EMD) de-noising method based on singular spectrum analysis (SA). Firstly, noisy signals are decomposed into several intrinsic mode functions (IMF) by the EMD in this method. The first IMF is regarded as high-frequency noise and the noise energy included in other IMFs can be estimated. Then, the ratio of signal energy in each IMF can be calculated. Secondly, the SSA is implemented on each IMF with proper window length and parts of proper singular value decomposition (SVD) components are selected to reconstruct the IMF according to the ratio of signal energy in each IMF. Finally, the denoised signals are obtained by adding all the reconstructed IMF and the residue. Compared with the wavelet soft threshold method, the EMD soft threshold method and the EMD filter method, the proposed method is superior to other methods as a whole, so it is an effective signal de-noising method.