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Construction of high order balanced multiscaling functions via PTST
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Construction of high order balanced multiscaling functions via PTST
Yang Shouzhi 1  and Peng Lizhong 2
| (1) |
Department of Mathematics, Shantou University, Shantou, 515063, China |
| (2) |
LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China |
Received: 1 September 2005 Accepted: 13 February 2006
Abstract 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.
Keywords PTST - balanced order - approximation order - multiscaling functions
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