一种双小波基的构造方法

journal6 ›› 2005, Vol. 26 ›› Issue (2): 29-32.

一种双小波基的构造方法

(1.株洲工学院计算机系，湖南株洲 412008;2.广东商学院数学系,广东广州 510320;3.华南理工大学计算机工程与应用系，广东广州 510641；4.广州航海高等专科学校计算机与信息工程系，广东广州 510725)

出版日期:2005-04-15 发布日期:2012-09-22
作者简介:江力(1969-)，男，湖南省耒阳市人，株洲工学院讲师，博士生，主要从事信号与图象处理、小波分析研究.
基金资助:
湖南省自然科学基金资助项目(04JJ3052)

A Construction Method of the Pairs of Wavelet Bases

(1.Dept. of Computer,Zhuzhou Institute of Technology,Zhuzhou 412008,Hunan China;2.Dept. of Mathematics,Guangdong Business College,Guangzhou 510320,China;3.College of Computer Science and Engineering,South China University of Technology,Guangzhou 510641,China；4.Dept. of Computer and Information Engineering,Guangzhou Maritime College,Guangzhou 510725,China)

Online:2005-04-15 Published:2012-09-22

摘要/Abstract

摘要：根据双尺度方程导出的尺度函数的Fourier变换无穷乘积公式，结合函数与函数的Hilbert变换之间的Fourier变换关系，提出了由2个共扼正交滤波器所构造的2个小波基是双小波基的一个条件，并通过满足该条件的例子来设计了满足该条件的具有最小长度的这种类型的2个滤波器的求解方法.

关键词： Hilbert变换, 双尺度方程, 双小波变换, 共扼正交滤波器

Abstract: According to the infinite product formula of scaling function's Fourier transform，combined with the Fourier transform relation between a function and its Hilbert transform，the paper derived an condition on how two wavelet bases constructed from two conjugate quadrature filters can be pairs of wavelet bases，and proposed a method on how to construct the pairs of wavelet bases.At the same time，a discrete numerical solution for the filters h0 and g0 of minimal length that satisfy the derivate condition was presented.

Key words: Hilbert transform, two scale equation, pairs of wavelets transform, conjugate quadrature filter

江力, 黄辉, 胡桂武, 曾岫. 一种双小波基的构造方法[J]. journal6, 2005, 26(2): 29-32.

JIANG Li, HUANG Hui, HU Gui-Wu, ZENG Xiu. A Construction Method of the Pairs of Wavelet Bases[J]. journal6, 2005, 26(2): 29-32.