广义V-系统的构造及相应的快速变换  

The Construction of Generalized V-System and the Corresponding Fast Transformation

作　　者：宋瑞霞[1] 孙坦坦 孙相东 王小春[2] Song Ruixia;Sun Tantan;Sun Xiangdong;Wang Xiaochun(College of Sciences,North China University of Technology,Beijing 100144;College of Sciences,Beijing Forestry University,Beijing 100083)

机构地区：[1]北方工业大学理学院,北京100144 [2]北京林业大学理学院,北京100083

出　　处：《计算机辅助设计与图形学学报》2018年第5期808-815,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家重点研发计划(2017YFF0209806)

摘　　要：为了深入研究信号分析中有效的数学工具——正交函数和正交变换,从Legendre正交多项式出发,构造一类由分段多项式组成的正交函数系,称之为广义k次V-系统,并指出它与k次V-系统的等价关系.首先给出广义k次V-系统对应的离散矩阵,用于广义k次V-变换;然后证明了在保持V-变换的几乎全部特点的同时,广义V-变换还具有快速算法,弥补了V-系统不容易设计快速算法的缺憾.实验结果表明,快速广义V-变换比V-变换在时间效率上有明显提高.To explore the effective mathematical tools(orthogonal function and orthogonal transformation)for signal analysis more deeply,a new orthogonal functions system composed of piecewise polynomials is constructed from the Legendre polynomials,and it is called generalized V-system of degree k.Equivalence relation between the generalized V-system of degree k and the V-system of degree k is proved.The discrete matrix corresponding to the generalized V-system of degree k is built,by which the generalized V-transform of degree k is constructed.It is proved that the generalized V-transform maintains almost all the properties of the V-transform,and also has a fast algorithm for degree one,which makes it superior to the V-transform as designing fast algorithms for the V-transform is difficult.The experimental results show that the time efficiency of the fast generalized V-transform is substantially increased compared with the V-transform.Key words:orthogonal functions;U-system;V-system;generalized V-system;fast algorithm 1相关工作正交

关 键 词：正交函数系 U-系统 V-系统 广义V-系统 快速算法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]