基于SVD的周期干净信号快速分解

摘要

This paper presents a method to decompose periodic and clean signal rapidly based on SVD. Firstly,the paper used SVD to reduce the noise of periodic source signal,and then applied SVD to get singular values of periodic and clean signal. Depend on the number of most frequencies,we divided singular values into groups. Therefore,we can restore every sub-signal sequences(number of sub-signals=number of most frequencies). Next,we used trigonometric functions to fit all sub-signal sequence,which can get fitting functions of sub-signal sequences.Finally,we made all fitting functions accumulated,which obtained expression form of fitting function of periodic and clean signal. Through practical example,the method has a certain practical significance for engineering applications.%文中提出了一种利用SVD将周期干净信号进行快速分解的方法.该方法首先利用SVD将带噪声的周期源信号进行降噪,然后将降噪后的周期干净信号进行SVD,并将奇异值按主频个数进行两两分组,由此依次还原出各个子信号序列(子信号个数=主频个数).接下来,对各个子信号序列进行三角函数拟合,从而得到各个子信号的拟合函数.最后将各个拟合函数进行累加,从而得到降噪后的周期干净信号的拟合函数表达式.经实例验证,该方法实践效果较好,对于工程应用有着一定的实际意义.