摘要
①给出了广义插值的概念 ,讨论了广义插值特性和正交性、紧支性、对称性之间的关系 ,建立了多尺度函数具有广义插值正交和广义插值对称的充要条件 ,结果表明它极大地克服了目前多小波取样定理研究领域存在的不足———基于插值特性的取样拒绝了众多性质优美的小波 ,也拒绝了信号处理愿望的对称性 ②给出了满足给定优美性质的多小波的高效构造方法———Hopfield反馈型神经网络法 ,与目前广为使用的利用Singular软件求Gr bner基方法相比 ,该方法不仅极大地减少了时间复杂度 。
Firstly, the concept of cardinal multiwavelets is given. In addition, the properties of this kind of multiwavelets are investigated. And the sufficient and necessary conditions for multiwavelets with general cardinal and orthogonal properties and those with general cardinal and symmetric properties are establisbed, which can overcome the shortcoming of the present sampling theorem for multiwavelets: there is no multiwavelets with cardinal and symmetric properties simultaneously until now. Secondly, since the construction of multiwavelets with some specified property requires the solution of a large and complex system of nonlinear design equations, Hopfield feedback neural networks are used instead of using software Singular, which is in most common use at present, to construct the multiwavelets. The experiments show that the method can not only offer the satisfactory solutions when the proper initial values are chosen, but also overcome the mass time-cost by using Singular to carry out the Grbner basis computations.
出处
《计算机研究与发展》
EI
CSCD
北大核心
2003年第6期861-868,共8页
Journal of Computer Research and Development
基金
国家自然科学基金 ( 69875 0 14 )
教育部骨干教师资助计划 (GG 5 2 0 10 5 30 10 2 2 )
湖南省自然科学基金 ( 0 0JJY2 0 5 8)
