基于正弦和余弦函数的小波滤波器的统一解析构造

基金项目: 国家自然科学基金资助项目(69903012,69682011);后勤工程学院科学研究基金资助项目

Uniform Analytic Construction of Wavelet Analysis Filters Based on Sine and Cosine Trigonometric Functions

1.
International Centre for Wavelet Analysis and Its Applications, Logistical Engineering University, Chongqing 400016, P R China;
2.
Department of Computer Science, Hong Kong Baptist University, Hong Kong, P R China;
3.
Department of Applied Mathematics, Chengdu Electronic University of Science and Technology of China, Chengdu 610054, P R China

摘要: 首次提出用正弦函数和余弦函数解析构造任意长度的紧支集正交小波滤波系数。首先给出了对N=2^k-1时(k个参数)的解析结构,其次给出了N=2k时正交小波滤波器的统一构造方法。此后验证了著名的Daubechies小波滤波器的构成参数,并验证了一些被广泛使用的著名小波分析滤波器,所有这些滤波器容易用一组参数直接计算出来。小波滤波器的解析构造使得在应用中动态选择小波基变得极其容易,这一结果必将在小波理论、应用数学及模式识别等领域产生十分重要的作用。
- 小波分析 /
- 滤波器 /
- 三角函数 /
- 解析构造
Abstract: Based on sine and cosine functions,the compactly supported orthogonal wavelet filter coefficients with arbitrary length are constructed for the first time.When N=2^k-1 and N=2k,the unified analytic constructions of orthogonal wavelet filters are put forward,respectively.The famous Daubechies filter and some other well known wavelet filters are tested by the proposed novel method which is very useful for wavelet theory research and many application areas such as pattern recognition.
- wavelet analysis /
- filter /
- trigonometric functions /
- analytic construction

[1]	Daubechies I.Orthonormal bases of compactly supported wavelets[J].Comm Pure and Appl Math,1988,41:909-996.
[2]	程正兴.小波分析算法与应用[M].西安:西安交通大学出版社,1998,78-119.
[3]	秦前清,杨宗凯.实用小波分析[M].西安:西安电子科技大学出版社,1994,41-53.
[4]	Wickerhauser M V.Adapted Wavelet Analysis From Theory to Software[M].New York:SIAM,1994,442-462.
[5]	Vaidyanathan P P,Huong P Q.Lattice structures for optimal design and robust implementation of two channel perfect-reconstruction QMF banks[J].IEEE Trans,on ASSP,1998,36(1):81-94.
[6]	李建平.小波分析与信号处理--理论、应用及软件实现[M].重庆:重庆出版社,1997,96-101,282-298.
[7]	李建平,唐远炎.小波分析方法的应用[M].重庆:重庆大学出版社,1999,72-91.
[8]	李建平.矢量积小波变换及小波分析的理论与应用研究[D].博士学位论文.重庆:重庆大学,1998.
[9]	TANG Yuan-Yan.Wavelet Theory and Its Application to Pattern Recognition[M].Singapore:World Scientific,1999.

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