连续小波变换的一维信号检测

奇异点是各种瞬态信号的主要特征,奇异点的类型多种多样。为了更准确地描述信号,分析局部奇异特征显得异常重要。在数学上,利用李氏(Lipschitz)指数来描述奇异性;Mallat等已证明通过不同尺度下的小波局部模极大值的衰减特征可求得李氏指数。讨论了利用小波模极大值理论,在尺度对数与小波系数对数的平面中具体求解李氏指数的数值算法过程并且给出了一个一维信号的Matlab仿真实验。实验结果表明该方法对李氏指数(Lip0.3<α<2)的测试有较高的精度。

Measurement of 1-D signal based on continuous wavelet transform

Sharp point variation is one of the most important characteristics of the nonstationary signals, and the local singularity analysis is very important for describing the signal more accurately. In mathematics, singularity can be described by lipschitz exponents . Mallat has proved that the lipschitz exponents can be obtained by calculating the decay of the local module maximum of the wavelet transform coefficients. In this paper, the numerical measurement procedure of the lipschitz exponents is provided and the simulation of a 1-D signal by Matlab is also given. The simulation shows that this method is precise to measure the lipschitz exponents, especially for lipschitz exponents between 0.3 and 2.0.