Fast algorithms of both discrete and orthonormal wavelet and wavelet packet coefficient are diagrammatized to be introduced . daubechies wavelet is applied to help to discuss the application and test on signal filtering and noise reduction with the principle and threshold implementation ; the basic principle to pickup the fault characteristics is introduced mainly about the relations between the maximum module and signal saltation point and how to characterize the saltation point with lipschitz exponent 展示了离散正交小波变换的mallat快速算法和小波包系数分解的快速算法；重点应用daubeches小波探讨了小波变换在信号滤波去噪中的应用和实验，阐述了其基本原理和通过阈值化处理实现滤波的具体方法；探讨了用小波变换进行故障特征提取的原理，说明了小波变换模极大值和信号突变点之间的关系以及怎样用李氏指数来表征突变点的性质。
