关键词: 信号的奇异性, 小波变换, 奇异点检测

Abstract: 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.

Key words: singularity of signal, wavelet transform, singular point detection