Singularity detecting with the second generation wavelet

Adopting the lifting scheme, introduced by Sweldens, a new wavelet is constructed. It overcomes the shortcoming of the classical wavelets that has no flexibility in the number of vanishing moment. Two examples are given to prove the second-generation wavelets's potentialities in the singularity detection of signal: a wavelet with vanishing moment and symmetry can be constructed according to the problem. Foundation item: Supported by the National Natural Science Foundation of China (19602014) Biography: XU Bing-lian (1977-), female, Master candidate, research direction: the wavelets application.