Optimal Wavelets Vanishing Moments for Singular Signal Detection

The wavelet transform modular maximum corresponds to the singularity of signal. Based on the fact that wavelet transform modular maximum of signal is different from that of noise at different scales, the noise can be removed from signal. The relationship between wavelet with different vanishing moments and Lipschitz exponent is discussed. And the influence of vanishing moments on singular signal detection is analyzed. The experimental results show that it is necessary to choose appropriate wavelets with different vanishing moments to detect signals with different singularities.