基于小波的信号突变点检测算法研究

Research on the Wavelet-Based Algorithms for Signal Singularity Detection

本文利用小波多分辨分析的特性将突变信号进行多尺度分解,然后通过分解后的信号来确定突变信号的突变位置。Lipschitz指数被用来定量描述函数的奇异性。当小波变换尺度越来越精细时,小波变换模极大值信号突变点的衰减速度取决于信号在突变点的Lipschitz指数。小波变换不仅可以确定突变点发生的时间,而且可以进一步判断突变的性质。

The paper uses the characteristics of wavelet multiresolution to decompose singularity signals , and locates the singularity positions of singularity signals using the decomposed signals. The Lipschitz index is used to describe the function singularity quantitatively. When the wavelet transform scale becomes tinier and tinier, the maximum signal singularity points＇ attenuation speed of the wavelet transform modulus depends on the Lipschitz index of the relevant singularity point. Wavelet transform can not only decide the generation time of the singularity point, but also judge the singularity property further.