| 一类正交函数系的离散表示及快速变换 |
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| 引用本文： | 王小春,宋瑞霞.一类正交函数系的离散表示及快速变换[J].计算机工程与应用,2008,44(8):40-44. |
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| 作者姓名： | 王小春 宋瑞霞 |
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| 作者单位： | 1. 北京林业大学,理学院,北京,100083
2. 北方工业大学理学院,北京,100041 |
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| 基金项目： | 国家重点基础研究发展规划（973）（the National Grand Fundamental Research 973 Prograln of Chinaunder Grant No.2004CB318000）;国家自然科学基金（the National Natural Science Foundation of China under Grant No.60133020.No.10671002,No.10771002）;浙江大学CAD＆CG国家重点实验室开放课题（No.A0503）;澳门科技发展基金（No.045/2006/A） |
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| 摘 要： | V系统是L20,1]上一类新的完备正交函数系,它由分段多项式组成,具有多分辨分析特性和全局/局部性,在几何模型的正交表达方面具有明显的优势,但其快速算法难以得到。利用Haar函数和Legendre多项式构造了一类由分段次多项式组成的函数系(文中称为W系),在该函数系上作函数逼近的效果等同于在V系统上的效果,并进一步讨论了一次离散W变换的快速算法,从而部分克服了直接对V系统设计快速算法的困难。
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| 关 键 词： | 正交完备函数系 V系统 Haar函数系 离散快速算法 W系 |
| 文章编号： | 1002-8331（2008）08-0040-05 |
| 收稿时间： | 2007-09-21 |
| 修稿时间： | 2007-12-03 |
Discrete representation and fast algorithm of new class of orthogonal system |
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| WANG Xiao-chun,SONG Rui-xia.Discrete representation and fast algorithm of new class of orthogonal system[J].Computer Engineering and Applications,2008,44(8):40-44. |
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| Authors: | WANG Xiao-chun SONG Rui-xia |
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| Affiliation: | 1.College of Sciences，Beijing Forestry University，Beijing 100083，China 2.College of Sciences，North China University of Technology，Beijing 100041，China |
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| Abstract: | V system is a new class of complete orthogonal system,which consists of piecewise polynomials in L20,1].The V system has multiresolution property and global/local property.It also has great advantages in representing geometric models.However,the fast algorithm of V transform is difficult to design.Using Haar functions and Legendre polynomials a new class of function system,W system,is constructed in this paper,which consists of piecewise polynomials.The approximating effect by W series is the same as that by V series.In this paper,the fast algorithm of discrete W transform of degree 1 is proposed,which partially solves the difficulties in directly designing the fast algorithm of V system. |
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| Keywords: | complete orthogonal function system V system Haar System discrete fast algorithm W system |
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