Abstract: A symmetrical second-generation wavelet dec with two vanishing moments is constructed accroding to the lifting scheme, and is applied to the singularity detection of signal. Compared with the detection effect of the DB2 wavelet, DEC and DB2 can detect the singularity point of signal correctly. But as far as the computation of Lip exponent is concerned, the computational accuracy of DEC is suprier to that of DB2 and most of classical wavelets and only inferior to that of the Mexh wavelet. But the Mexh wavelet hasn’t compact support and only has zero vanishing moment. The experimental data show that the second-generation wavelet DEC is more fit for the singularity detection of signal than most of classical wavelets.

Key words: lifting scheme, second-generation wavelet, singularity, classical wavelet, Lip exponent

摘要： 利用提升格式原理构造了一个对称的具有二阶消失矩的第二代小波DEC，并将其应用于信号的奇异性检测。与经典小波DB2的检测效果相比较，两者都可以准确地检测出信号的奇异点，但在Lip指数的计算方面，DEC比DB2以及其他大部分经典小波的准确性要强得多，仅次于墨西哥草帽小波。但是墨西哥草帽小波是一个非紧支集且只有零阶消失矩的小波。实验结果表明，第二代小波DEC比大部分经典小波更适合于信号的奇异性检测。

关键词: 提升格式, 第二代小波, 奇异性, 经典小波, Lip指数