Construction of high order balanced multiscaling functions via PTST  

作　　者：YANG Shouzhi PENG Lizhong 

机构地区：[1]Department of Mathematics, Shantou University, Shantou 515063, China [2]LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China

出　　处：《Science in China(Series F)》2006年第4期504-515,共12页中国科学（F辑英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.90104004 and 10471002);the 973 Project of China(Grant Nos.G1999075105);the Natural Science Foundation of Guangdong Province(Grant Nos.032038,05008289);the Doctoral Foundation of Guangdong Province(Grant No.04300917).

摘　　要：The concept of paraunitary two-scale similarity transform （PTST） is introduced. We discuss the property of PTST, and prove that PTST preserves the orthogonal, approximation order and smoothness of the given orthogonal multiscaling functions. What is more, by applying PTST, we present an algorithm of constructing high order balanced multiscaling functions by balancing the already existing orthogonal nonbalanced multiscaling functions. The corresponding transform matrix is given explicitly. In addition, we also investigate the symmetry of the balanced multiscaling functions. Finally, construction examples are given.The concept of paraunitary two-scale similarity transform （PTST） is introduced. We discuss the property of PTST, and prove that PTST preserves the orthogonal, approximation order and smoothness of the given orthogonal multiscaling functions. What is more, by applying PTST, we present an algorithm of constructing high order balanced multiscaling functions by balancing the already existing orthogonal nonbalanced multiscaling functions. The corresponding transform matrix is given explicitly. In addition, we also investigate the symmetry of the balanced multiscaling functions. Finally, construction examples are given.

关 键 词：PTST balanced order approximation order muitiscaling functions. 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]