联系Butterworth滤波器的双正交小波(英文)  

Bi-orthogonal Wavelets Related to Butterworth Filters

作　　者：胡琳[1] 刘有明[1] 

机构地区：[1]北京工业大学应用数学系,北京100022

出　　处：《数学进展》2007年第3期309-320,共12页Advances in Mathematics（China）

基　　金：The project is partially supported by a grant from Beijing Educational Committee(No.KM200410005013);NSFC(No.10671008);Beijing Program of"Ren Cai Qiang Jiao".

摘　　要：联系Butterworth滤波器的双正交小波称为Butterworth小波,它们具有很好的性质:包括对称性,插值性及消失矩．本文定义了离散空间L^2(Z)中的双正交小波并给出一个易于验证的充分条件．利用这一条件,重新得到Butterworth小波;进一步,构造了一类双正交小波．它们不仅具有Butterworth小波的前述所有性质,而且具有最短可能的支集．Butterworth filters are related to some bi-orthogonal wavelets, called Butterworth wavelets. Those wavelets have nice properties which include symmetry, the interpolation and vanishing moments. In this paper, a general concept for bi-orthogonal wavelet bases in l^2（Z） is introduced and an easily checked sufficient condition is given, by which the Butterworth wavelets are derived; then a family of bi-orthogonal wavelets are constructed, which have all properties of the Butterworth wavelets; Moreover, our wavelets have the shortest possible supports.

关 键 词：Butterworth小波 离散傅立叶变换 对称性 插值性 消失矩 

分 类 号：O174.2[理学—数学]