滤波器长度与消失矩对双正交小波构造的影响  

Effects of filter length and vanishing moment on the construction of biorthonormal wavelets

作　　者：梁茜[1] 丁宣浩[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2007年第1期60-63,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(10361003);广西自然科学基金(0542046);广西研究生教育创新计划项目(2006105950701M03)

摘　　要：通过进一步研究如何构造有一定滤波器长度和消失矩阶数的小波,在构造具有消失矩的小波时发现,偶数长对称小波的消失矩仅需其偶数阶导数满足要求,奇数长时仅需奇数阶导数满足要求,这样可以节约一半的计算量。另外根据奇数长对称的例子研究了一定偶数长度的双正交对称小波能够具有多少阶消失矩,以及该小波具有怎么样的形式。Several good quality biorthonormal bases of compactly supported symmetrical wavelets with high-ordered vanishing moment had been constructed before. However, further study needs to be done regarding how filter length and vanishing moment influence the construction of these wavelets. Our study leads us to such a finding that in constructing even length and odd length symmetrical wavelets with vanishing moment respectively only the evenorder and odd-order derivatives are needed respectively. The quantity of computation can thus be cut down to a half. We have also studied a few examples and obtained results of the format of these wavelets as well as the number of order of vanishing moment.

关 键 词：双正交小波 消失矩 滤波器长度 

分 类 号：O174.3[理学—数学]