【作者】 李和平；

【导师】 杨万年；

【作者基本信息】 重庆大学 ， 运筹学与控制论， 2002， 硕士

【摘要】 本文的主要工作分为两个部分：首先，我们介绍了改进遗传算法IGA并把它应用于最优小波基的选取。通过将信号用小波级数展开后得到其在某个期望尺度上的近似表示，由此建立一个表达信号与其近似之间误差的代价函数，然后我们利用改进遗传算法最优化此代价函数以获得全局最优的正交小波基。其次，讨论了紧支集正交小波的对称化问题。本文提出一种新的对称化方法，把一大类紧支集实值的非对称正交小波函数分解成对称和反对称两部分，并证明了其相应的两部分仍然构成对称和反对称的紧支正交小波基，而且我们发现尺度函数对称和反对称部分分别是某子空间的尺度函数和小波函数。更多还原

【Abstract】 The research of this paper can be divided into three parts. Firstly, we will introduce IGA (Improved Genetic Algorithm) and apply it to choosing the best wavelet’s basis. An optimal choice method of an orthogonal wavelet basis through genetic algorithms is presented in paper. By expanding the signal in wavelet series, we get its approximation up to a desired scale. And a cost function for representing the error between the signal and its approximation is established. We then optimize the cost function by Improved Genetic Algorithms in order to obtain the global optimal orthogonal wavelet basis. Secondly, the symmetrical prosperity of wavelet’s base is discussed in Chapter 3. This article shows a new method to construct symmetric compacted orthogonal wavelet packet basis ：the original compacted orthogonal wavelet basis and scaling function are decomposed into symmetric and anti-symmetric parts respectively ，then we prove that three of four parts is also wavelet basis and another is scale function. we find it simple to process 1-D signal. Finally, By these results above, all the results above are applied to DSP.更多还原