Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (31): 10-13.DOI: 10.3778/j.issn.1002-8331.2010.31.003

• 博士论坛 • Previous Articles     Next Articles

Design of even number rational symmetric compactly-supported biorthogonal wavelet filter

HAN Fang-fang1,2,DUAN Fa-jie1,ZHANG Bao-feng2,DUAN Xiao-jie1   

  1. 1.State Key Lab of Precision Measuring Technology & Instruments,Tianjin University,Tianjin 300072,China
    2.School of Electrical Engineering,Tianjin University of Technology,Tianjin 300384,China
  • Received:2010-06-28 Revised:2010-09-25 Online:2010-11-01 Published:2010-11-01
  • Contact: HAN Fang-fang



  1. 1.天津大学 精密测试技术与仪器重点实验室,天津 300072
    2.天津理工大学 自动化学院,天津 300384
  • 通讯作者: 韩芳芳

Abstract: Most wavelet filters that constructed based on Daubechies compactly-supported wavelet construction theory have nonlinear phase and irrational number coefficients.Nonlinear phase may cause distortion in image processing,and irrational filter coefficients will cause much inconvenience for wavelet applications on computer,especially for embedded processor applications.With thought of the theory of perfect-reconstruction filter banks,this paper does a study for linear phase biorthogonal perfect-reconstruction wavelet filter banks,and through of detail derivation,makes a conclusion for the procedure of even number rational coefficients symmetric compactly-supported biorthogonal wavelet filter construction,which can be achieved by adding some vanishing moments conditions.With the example of length 8-4 biorthogonal wavelet filters design,this paper makes a detail discussion on the value selection for free variable appears in design equations,and then deduces the length 8-4 rational biorthogonal wavelet filters models.

Key words: wavelet filter construction, rational number wavelet filter, even number symmetric filter, biorthogonal wavelet, wavelet transform

摘要: 基于Daubechies紧支集小波构造方法所得到的小波滤波器多为非线性相位和无理数系数。非线性相位滤波器在图像处理过程中容易引起失真,而无理系数滤波器给小波变换的应用尤其是在算法的硬件实现方面带来不便。借助完全重构滤波器思想,进行了具有线性相位的双正交小波滤波器设计,同时通过添加消失矩特性条件,归纳推导出偶数长有理系数双正交对称紧支集小波滤波器的构造方法。以长度为8-4双正交小波设计为例,对设计方程中出现的自由变量的取值范围进行了讨论,得到了8-4有理系数双正交对称小波滤波器。

关键词: 小波滤波器构造, 有理系数小波滤波器, 偶数长滤波器, 双正交小波, 小波变换

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