小波分析中小波基构造方法的研究进展与展望

Progress and Prospect of Wavelet Bases Construction Methods in Wavelet Analysis

小波分析中的小波基具有不唯一性,用不同的小波基分析同一个问题会产生不同的结果。如何根据实际问题构造最优小波基一直是小波研究的热点及难点。通过总结小波基构造方法的研究现状,分析目前小波基构造方法存在的不足,在此基础上提出了一种从实际信号特征出发、与被分析信号相似度高、能广泛应用到不同类型信号分析中的小波基构造思想,为小波基的构造拓展了思路。

Different wavelet bases would result in different outcomes even for same problem since it had the characteris- tic of non-unique in wavelet analysis. How to construct opti- mal wavelet basis according to actual problem has been a hotspot and difficult issue in the wavelet research. The shortcomings in current construction methods of wavelet ba- ses were analyzed by summarizing the present research sta- tus. On basis of that, a new method of wavelet bases con- struction was proposed, which derived from the actual signal characteristics, is highly similar to analyzed signal, and can be widely applied to analyze different types of signal. This method offered a new approach to wavelet bases construc- tion.