对称反对称多重尺度函数的构造

１　多重小波的定义和双尺度相似变换 作为一种分析工具，小波已经运用在各种领域，并取得了显著的成果．近年来，多重小波成为小波研究的热点．Ｉ．Ｄａｕｂｅｃｈｉｅｓ［１］已经证明，对单重小波，除Ｈａｒｒ基外不存在对称和反对称的有紧支集的小波正交基．而多重小波则不受这一限制． 利用分形插值的方法，Ｇｅｒｏｎｉｍｏ、Ｈａｒｄｉｎ和 Ｍａｓｓｏｐｕｓｔ［２］等构造出了ＧＨＭ多重小波，相应的多重尺度函数和多重小波函数如图１和图２所示．ＧＨＭ多重小波的两个尺度函数都是对称的，相应的小波函数则一个对称另一个反对称；…

CONSTRUCTION OF SYMMETRY AND ANTI-SYMMETRY MULTISCALING FUNCTIONS

Multiwavelets is the new direction of wavelets research. It possesses many good properties which scalar wavelets dose not. But there are some problems in the construction of high approximation order multiwavelets. This paper gives a construction method of high approximation order multiscaling functions using Two-scale Similarity Transform, then gives a detailed argumentation of the choice of the transform matrix. At last, the paper constructs a multiscaling function with approximation order 3 by using previous method.