| 基于尺度函数的插值小波构建方法 |
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| 引用本文： | 张治国,胡学海,周依.基于尺度函数的插值小波构建方法[J].电子科技大学学报（自然科学版）,2017,46(4):481-487. |
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| 作者姓名： | 张治国 胡学海 周依 |
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| 作者单位： | 电子科技大学自动化工程学院 成都 611731 |
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| 基金项目： | 国家自然科学基金60904072国家自然科学基金71301018 |
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| 摘 要： | 经典小波采样理论应用正交小波构建插值小波，然而正交小波的解析表达式通常比较复杂或难以获得，因此在实践中确定和构建插值小波，成为信号处理及调和分析领域研究的重要课题。为此，提出一种构建插值小波的新方法。该方法应用尺度函数构建插值小波，避免了对正交小波的求解，提高了构建插值小波的效率。以Daubechies和Coiflets多分辨分析为例，验证了该方法的正确性和有效性。
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| 关 键 词： | 插值基 插值小波 多分辨率分析 小波采样 |
| 收稿时间： | 2016-05-31 |
A Construction Method of Interpolatory Wavelet Based on Scaling Function |
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| Affiliation: | School of Automation Engineering, University of Electronic Science and Technology of China Chengdu 611731 |
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| Abstract: | In classical wavelet sampling theory, interpolatory wavelets are constructed by using orthogonal wavelets. Since the analytic expressions of orthogonal wavelets are usually complex or unavailable, interpolatory wavelet construction has become an important topic in signal processing and harmonic analysis. In this paper, a new method is proposed to construct interpolating wavelets from scaling functions. Since this method has avoided using orthogonal wavelets in construction of interpolation wavelets, it can greatly improve efficiency of interpolating wavelet construction. Taking Daubechies and Coiflets MRAs as examples, our method is verified to be effective for interpolatory wavelet construction. |
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