无显式表达小波基的参数方程

对无显式表达小波基的参数形式进行研究，得到了几种具有不同数目参数的小波基参数方程，同时对具有消失矩限制的小波基参数方程进行了研究。利用这些参数方程，给出了一个用不同参数而得到的两个小波基对同一个信号进行分解的对比实例，此实例说明参数的选择对于小波分解的效果起着决定性作用，通过对参数的适当选择可以实现对信号的最佳小波基分解。

Parametric Equation of Wavelet Bases without Analytic Equation

The parametric form of wavelet bases without analytic equation is studied in this paper. By virtue of the polyphase representation of orthonormal wavelet, this paper gives detailed method to obtain wavelet bases' parametric equations. Several wavelet bases' equations, with different number of parameters are obtained according to this method. Furthermore, the parametric equations of wavelet bases that have the limitation of vanishing moment are discussed also. An example of a signal decomposed by two wavelet bases with different parameters is given. The analysis result shows that different parameters make wavelets have different time-frequency characteristics and make signal's wavelet decomposition have different effect, so the selection of parameter have the decisive influence on the wavelet's decomposing effect. Through the proper selection of the parameter, the optimal effect of signal decomposition using wavelet can be obtained.