Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1481-1492.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 42A99
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