摘要
利用W.Swelden和M.J.Shensa关于插值性的刻画,证明了不存在具有3个生成元且满足插值性的小波紧框架.在满足近似插值性及较高阶消失矩的性质下,设计一个低通滤波器,利用不等式得到3个滤波器,从而得到小波紧框架.所得的高通滤波器中有一个满足对称性,一个满足反对称性.设计所得到的滤波器都含有一个自由参数,此参数的引入增加了小波框架的选择余地.
Using the demonstration about the interpolation of W. Swelden and M. J. Shensa , we prove that the interpolated wavelet tight frame generated by three generators does not exist. Under satisfying nearly interpolation and higher vanishing moment, we design a low-pass filter, and then using an inequality giving by Ron, we will get three high-pass filters. Therefore we can get the wavelet tight frames that satisfy our properties. Two of those high-pass filters satisfy symmetry or antisymmetry, and all of them have a free parameter. The greater freedom will widen the selection of both low-pass and high-pass filters. Finally, we give the algorithm for filters and some concrete examples of wavelet tight frames.
出处
《西安电子科技大学学报》
EI
CAS
CSCD
北大核心
2006年第4期665-669,共5页
Journal of Xidian University
基金
国家自然科学基金资助项目(10571113)
关键词
小波紧框架
消失矩
对称性
插值性
wavelet tight frame
vanishing moment
symmetry
interpolation
