数学物理学报 ›› 2014, Vol. 34 ›› Issue (6): 1481-1492.

• 论文 • 上一篇    下一篇

L2(R2)中2进变元低通滤波器

李忠艳1|施咸亮2   

  1. 1.华北电力大学 数理学院数理系 北京 102206; 2. 湖南师范大学数学与计算机科学学院, 高性能计算与随机信息处理省部共建教育部重点实验室(HPCSIP) 长沙 410081
  • 收稿日期:2013-03-19 修回日期:2014-06-24 出版日期:2014-12-25 发布日期:2014-12-25
  • 基金资助:

    国家自然科学基金(11101142, 11071065, 11171306)和中国博士后科学基金(20100480942)资助

On Dyadic Bivariate Low Pass Filters in L2(R2)

 LI Zhong-Yan1, SHI Xian-Liang2   

  1. 1.Department of Mathematics and Physics, North China Electric Power University, Beijing 102206;
    2.College of Mathematics and Computer Science, Key Laboratory of High Performance Computing and Stochastic
    Information Processing (HPCSIP)(Ministry of Education of China) Hunan Normal University, Changsha 410081
  • Received:2013-03-19 Revised:2014-06-24 Online:2014-12-25 Published:2014-12-25
  • Supported by:

    国家自然科学基金(11101142, 11071065, 11171306)和中国博士后科学基金(20100480942)资助

摘要:

一维2进低通滤波器在一维多分辨分析(MRA)小波的构造和拓扑性质研究中起到重要作用. 对于高维小波,其生成要依赖于
某个扩张矩阵, 所以构造比较复杂. 该文讨论由一致矩阵2I2=(2 0 0 2)生成的MRA小波的低通滤波器(称作2进双变量滤波器).
利用2进双变量滤波器乘子完全刻画了2进双变量滤波器, 并且证明了所有2进双变量滤波器集合在L2(T2)范数拓扑下是道路连通的结论

关键词: 2进双变量低通滤波器, 2进MRA, 滤子乘子

Abstract:

The low pass filters play important role in construction of wavelets with MRA. But construction of wavelets of MRA in high dimensional case is very complicate in view of their different dilation matrices. In this paper, we discuss the low pass filters of MRA multivariate wavelets with the uniform dilation matrix 2I2=(2 0 0 2) (These filters are called  dyadic bivariate filters). We character dyadic bivariate filters by using dyadic bivariate filter multipliers and prove that the set of all
dyadic bivariate low pass filters is path-connected under the norm L2(T2) topology.

Key words: Dyadic bivariate low pass filters, Dyadic MRA, Filter multipliers

中图分类号: 

  • 42A99