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.
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).
