Abstract: This paper gives several non-linear difference equations based on the orthogonality，regularity and standardity of the orthogonal wavelet with compact support.Then the paper designs a least square objective function from these equations and optimize it by the Gauss-Newton algorithm.However，because of local convergence of Gauss-Newton algorithm，the paper combines the Gauss-Newton algorithm with the stochastic algorithm to get a more feasible algorithm.This algorithm can not only approximate the solutions well given by Daubechies，but also give wavelets which have better symmetricality and locality.Finally，the algorithm proposed can also be used to construct the biorthogonal wavelet or multiwavelet.

Key words: orthonormal wavelet basis, optimization, stochastic algorithm

摘要： 从紧支撑正交小波滤波器的正交性、规范性及正则性条件出发，获得了求解滤波器系数的非线性差分方程组，并采用最优化方法求解。由于该优化问题的目标函数是具有零残数的最小二乘，可以用Gauss-Newton法求解。为了克服Gauss-Newton法的局部收敛性，结合随机算法和Gauss-Newton法形成了一种更为可行的算法。它不仅计算出了Daubechies小波的滤波器系数，还可以得到其他对称性与局部性更好的小波。另外，该算法还可以用于双正交或多小波滤波器的构造，具有很好的可移植性。

关键词: 正交小波基, 最优化, 随机算法