无显式表达小波基的自适应选择

The Adaptive Selection of Wavelet Base without Analytic Equation

研究了无显式表达小波基的自适应选择问题。从不同应用角度定义了评价小波基分解效果的两种适应度函数 ;所给出的适应度函数曲面实例充分说明了对小波进行自适应选择的必要性。利用这两种适应度函数 ,提出了一种改进的遗传算法 ,对小波参数方程中的参数进行搜索 ,并利用适应度函数对搜索结果进行评价 ,实现了信号的自适应小波基分解 ,在此基础上给出了自适应小波基分解的实例 ,并与 Daubechies小波的分解结果进行对比 。

The adaptive selection of wavelet base without analytic equation is studied in this paper for the first time. In order to realize the adaptive selection of wavelet base, firstly two fitness functions are defined to appraise wavelet bases' decomposing effect from different applying purpose. Under certain circumstance if an approximate signal needs to be emphasised, then a fitness function is defined as:F(H)=∑x∈ZS^2 jf(x)/f^2(x),on the other hand while detailed signal must be stressed then another fitness function is defined as:F(H)=∑x∈ZW^2 jf(x)/f^2(x). An example of a signal's two fitness function surfaces given in this paper shows that it's very necessary for wavelet bases to be selected adaptively according to signal's feature in wavelet transformation. An improved genetic algorithm is proposed to search the parameters in wavelet parametric equation and at the same time the fitness function is used to appraise the searching effect. When the fitness suffices the concerted requirement then the optimal wavelet is searched, so signal's adaptive wavelet decomposition is brought into effect. One example of signal's adaptive wavelet decomposition is given based on this algorithm. Compared with Daubechies wavelet's decomposing method, the adaptive wavelet's decomposing method has clear advantages.