A general sampling theorem for multiwavelet subspaces

作     者：贾彩燕 高协平 

作者机构：TheKeyLaboratoryofIntelligentInformationProcessingInstituteofCOmputingTechnologyChineseAcademyofSciencesBeijing100080China InformationEngineeringCollegeXiangtanUniversityXiangta 

出 版 物：《Science in China(Series F)》 (中国科学（F辑英文版）)

年 卷 期：2002年第45卷第5期

页      面：365-372页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No. 69875014) and the Foundation of University Key Teacher by the Ministry of Education (Grant No. GG-520-10530-1022) 

主　　题：multiwavelet sampling theorem Zak transform general cardinal. 

摘      要：An orthogonal scaling function (?)(t) can realize perfect A/D (Analogue/Digital) and D/A if and only if (?)(t) is cardinal in the case of scalar wavelet. But it is not true when it comes to multiwavelets. Even if a multiscaling function ?(t) is not cardinal, it also holds for perfect A/D and D/A. This property shows the limitation of Selesnick s sampling theorem. In this paper, we present a general sampling theorem for multiwavelet subspaces by Zak transform and make a large family of multiwavelets with some good properties (orthogonality, compact support, symmetry, high approximation order, etc.), but not necessarily with cardinal property, realize perfect A/D and D/A. Moreover, Selesnick s result is just the special case of our theorem. And our theorem is suitable for some symmetrical or nonorthogonal multiwavelets.