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

LI Jian-ping; TANG Yuan-yan; YAN Zhong-hong; ZHANG Wan-ping

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Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(5): 504-518

LI Jian-ping, TANG Yuan-yan, YAN Zhong-hong, ZHANG Wan-ping. Uniform Analytic Construction of Wavelet Analysis Filters Based on Sine and Cosine Trigonometric Functions[J]. Applied Mathematics and Mechanics, 2001, 22(5): 504-518.

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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

Received Date: 2000-05-19
Rev Recd Date: 2001-01-10
Publish Date: 2001-05-15

Abstract

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

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References(9)

References

[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.