对称中心相同的正交平衡多小波的存在性及参数化  

EXISTENCE AND PARAMETERIZATION OF ORTHONORMAL BANLANCING MULTIWAVELETS WITH THE SAME SYMMETRIC CENTER

作　　者：江力[1] 朱善华[1] 吕勇[1] 

机构地区：[1]湖南工业大学理学院信息与计算科学系,株洲412007

出　　处：《高等学校计算数学学报》2011年第1期39-46,共8页Numerical Mathematics A Journal of Chinese Universities

基　　金：湖南省教育厅科研项目(09C319);国家自然科学基金项目(10971059)

摘　　要：1引言多小波因为可同时满足对称性、紧支撑性、高阶消失矩和正交性,所以在信号处理等应用方面比单小波更有优势,但是,基于多小波的信号处理需进行预滤波[1,2],而预滤波又会破坏所设计的多小波的正交性、对称性等特性,这阻碍了多小波的应用.文献[3]提出了平衡多小波的概念,应用平衡多小波进行信号处理时不但可以避免预滤波,而且在处理多项式信号时能被低通滤波器特征化,被高通滤波器取消;According to the parameterization results of m-channel causal finite impulse response orthogonal filter banks and the theory of balancing multiwavelets, the existence and parameterization of orthonormal banlancing multiwavelets with the same symmetric/antisymmetric center 1/2（1＋γ＋γ/m-1） for positive integer γ is studied. It is proved that there is no such orthonormal multiwavelets with the same symmetric/antisymmetric center as the product of the dilation factor m and the multiplicity r is odd and no such orthonormal balancing multiwavelets with the same symmetric/antisymmetric center as the dilation factor m is equal to three and the multiplicity r is even; For the case of dilation factor m being equal to four, we prove the existence of the orthonormal balancing multiwavelets of multiplicity r with the same symmetric/antisymmetric center and propose a parameterization theorem. A construction example for the dilation factor m being equal to four and multiplicity being equal to 2 is presented.

关 键 词：对称中心 正交平衡 多小波 存在性 参数化 

分 类 号：O174.2[理学—数学]