基于小波变换的奇异信号检测研究

Study on the Singular Signal Detection Based on Wavelet Transform

奇异信号的奇异点经常携带有比较重要的信息,它是信号的重要特征之一.证明了小波变换能用来检测信号的奇异性,利用小波变换模的极大值和信号奇异点的关系,可以分析信号局部奇异性.信号局部奇异性用李氏指数来描述.研究了奇异性检测小波基的选择条件.给出了实例分析,结果表明,小波变换在信号奇异性检测和局部化分析方面具有优异特性.

The singular points of the singular signal often take some important information, which is one of the main characters of a singular signal. It is proved that wavelet transform can be used to estimate the singularity. Using the relationship between wavelet transform modulus maxima and singular point, the signal singular point location can be analyzed; the local singularity is described by Lipschitz index. The qualifications of wavelet base for the singular signal detection are studied. The example is taken finally, and the conclusion that wavelet transform have specific property for singular signal detection and location analysis.