| 摘要: |
| 采样定理是现代信息理论与技术的基本工具,具有采样性质的信号具有比较完美的信息重构形式.Walter 和 Zhou 将古典信号的采样定理发展到小波子空间.发展了基于小波框架的数字信号的采样定理与方法.提出并回答了信息理论中的一个基本问题:一个能量有限的数字信号,是否具有采样定理的形式.以小波框架为工具给出了具有采样性质的数字信号的刻画;对于一个给定的采样子空间,给出了该子空间的信号的表示形式;特别是给出了一大类新的具有采样性质的数字信号空间.应用实例表明,从理论和实践上对于数据信息的采样和重构是有意义的,是对以往相关结果的有效改进. |
| 关键词: 小波框架 采样定理 小波子空间 平移不变子空间 信息重构 |
| DOI： |
| 分类号: |
| 基金项目:Supported by the National Natural Science Foundation of China under Grant Nos.60872161, 60572113 (国家自然科学基金) |
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| Sampling Subspaces Based on Wavelet Frames |
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YANG De-Yun,LI Xiu-Zhen,SANG Sheng-Jü,HOU Ying-Kun,LIU Ming-Xia
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| Abstract: |
| Sampling theory is one of the most powerful results in modern information theory and technology. The digital signal with sampling properties can be reconstructed from its samples in a perfect form. Walter and Zhou extended the Shannon sampling theorem to wavelet subspaces. This paper improves the classical sampling theorems based on wavelet frames. A basic problem on information theory is introduced here. For a given digital signal, whether it has sampling series form. In this paper, the digital signals with sampling properties are characterized based on wavelet frames. For a given sapling subspace, the analytic form of the signals in it is proposed. Especially some new kinds of sampling subspaces are offered here. As an application, the examples show that the new theorems improve some known relating results, which is effective for the digital signals’ sampling and reconstructions. |
| Key words: wavelet frame sampling theorem wavelet subspace shift-invariant subspace information reconstruction |
