计算机工程与应用 ›› 2008, Vol. 44 ›› Issue (8): 40-44.

• 学术探讨 • 上一篇    下一篇

一类正交函数系的离散表示及快速变换

王小春1,宋瑞霞2   

  1. 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
  • 收稿日期:2007-09-21 修回日期:2007-12-03 出版日期:2008-03-11 发布日期:2008-03-11
  • 通讯作者: 王小春

Discrete representation and fast algorithm of new class of orthogonal system

WANG Xiao-chun1,SONG Rui-xia2   

  1. 1.College of Sciences,Beijing Forestry University,Beijing 100083,China
    2.College of Sciences,North China University of Technology,Beijing 100041,China
  • Received:2007-09-21 Revised:2007-12-03 Online:2008-03-11 Published:2008-03-11
  • Contact: WANG Xiao-chun

摘要: V系统是L2[0,1]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k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。

Abstract: V system is a new class of complete orthogonal system,which consists of piecewise polynomials in L2[0,1].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.