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

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