信号奇异点的分步检测法

针对两种常见的信号奇异点：脉冲型奇异点和阶跃型奇异点，证明信号的奇异点与信号小波变换的最值有关，如果适当选择小波基函数，那么信号的脉冲奇异点将对应于小波基函数的最值点，而信号的阶跃奇异点将对应于小波基函数的原函数的最值点。据此，设计了一个新的基于小波变换的信号奇异点分步检测法（Hierarchical Singular Point Detection based on Wavelet Transform，HSPDWT），该方法的特点是根据脉冲奇异点和阶跃奇异点的不同特征分两步从信号中提取奇异点。仿真及真实信号上的实验证明了HSPDWT的可行性和有效性。

Hierarchical singular point detection based on wavelet transform

For two major classes of signal singular points, the pulse singular point and the step singular point, it is showed that the maximum absolute value of real wavelet transform can be used to detect the singularity in signal. It is further showed that, by using the wavelet basis function chosen carefully, the pulse singular point in signal exactly corresponds to the maximum absolute value point of the real wavelet basis function, and the step singular point corresponds to the maximum absolute value point of the primitive function of the real wavelet basis function. As a result, a hierarchical singular point detection method is developed. An important characteristic of the method is that in the course of singular point detection the singular points are detected step by step according to their features. The experimental results on a number of artificial and real signals are very encouraging and show the method can indeed identify the singularity from signals successfully.