| 带限函数外推算法收敛性研究 |
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| 引用本文： | 张兆田,渠刚荣,姜明. 带限函数外推算法收敛性研究[J]. 工程数学学报, 2004, 21(2): 143-148 |
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| 作者姓名： | 张兆田 渠刚荣 姜明 |
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| 作者单位： | 中国科学院自动化研究所,100080;北京交通大学,北京,100044;北京大学数学学院,北京,100871 |
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| 基金项目： | 国家自然科学基金项目(69931010,60372015,60272018),北京交通大学校基金项目(2002SM054),国家973项目(2003CB716101). |
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| 摘 要： | Gerchberg-Papoulis(G-P)算法是解决带限信号外推问题的一个广泛使用的迭代算法。在数据存在噪声时，本文论证了G-P迭代算法的收敛性不再成立，其原因是相应的线性算子在L^2范数下是非压缩算子，并以数值模拟说明了这一问题。针对这一问题，我们提出改进的Gerchberg-Papoulis(IG-P)算法，并研究了该算法在L^2范数下的收敛性质。数值模拟结果表明，IG-P迭代算法具有较好的信号分辨能力和收敛性质。
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| 关 键 词： | 带限函数 外推 迭代算法 收敛性 |
| 文章编号： | 1005-3085(2004)02-0143-05 |
| 修稿时间： | 2003-12-13 |
Convergence on Extrapolation for Band-limited Function |
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| ZHANG Zhao-tian,QU Gang-rong,JIANG Ming. Convergence on Extrapolation for Band-limited Function[J]. Chinese Journal of Engineering Mathematics, 2004, 21(2): 143-148 |
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| Authors: | ZHANG Zhao-tian QU Gang-rong JIANG Ming |
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| Affiliation: | ZHANG Zhao-tian~1,QU Gang-rong~2,JIANG Ming~3 |
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| Abstract: | The Gerchberg-Papoulis (G-P) algorithm is a widely applied iterative method for the extrapolation of band-limited signals. When the observed data are corrupted with noise, the G-P algorithm is not convergent any more because the corresponding linear operator is not contractive under the L~2 norm. This phenomenon is also illustrated with numerical simulation. We propose an improved Gerchberg-Papoulis(IG-P) algorithm and study its convergence properties. It is proved that the IG-P algorithm is convergent under the L~2 norm. Numerical stimulation is provided to demonstrate that the convergence and signal resolving power of I-GP are better than those of the original G-P algorithm when the data are corrupted with noise. |
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| Keywords: | band-limited signal extrapolation iterative algorithm convergence |
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