An Improved Nyquist–Shannon Irregular Sampling Theorem From Local Averages
An Improved Nyquist–Shannon Irregular Sampling Theorem From Local Averages
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DOI：
10.1109/tit.2012.2199959
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发表时间：
2012-09
影响因子：
2.5
通讯作者：
Zhanjie Song;Bei Liu;Yanwei Pang;Chunping Hou;Xuelong Li
中科院分区：
文献类型：
--
作者：
Zhanjie Song;Bei Liu;Yanwei Pang;Chunping Hou;Xuelong Li
Nyquist-Shannon采样定理是关于从均匀采样的样本中重构带限信号。信号带宽越高，均匀采样可能变得越困难。为了解决这个问题，文献中已经研究了基于局部平均的信号重构。本文从一般的局部平均出发，得到了一个改进的Nyquist-Shannon抽样定理。在实践中，测量设备在不对称的间隔上给出加权平均值。作为特例，对于对称区间的局部平均，我们证明了其采样率远低于Gröchenig的一个结果。此外，我们从局部平均得到了两个精确的对偶框架，其中一个改进了孙和周的结果。在本文的最后，作为局部平均抽样的一个应用实例，我们考虑了一种重建算法：分段线性逼近。
The Nyquist–Shannon sampling theorem is on the reconstruction of a band-limited signal from its uniformly sampled samples. The higher the signal bandwidth gets, the more challenging the uniform sampling may become. To deal with this problem, signal reconstruction from local averages has been studied in the literature. In this paper, we obtain an improved Nyquist–Shannon sampling theorem from general local averages. In practice, the measurement apparatus gives a weighted average over an asymmetrical interval. As a special case, for local averages from symmetrical interval, we show that the sampling rate is much lower than that of a result by Gröchenig. Moreover, we obtain two exact dual frames from local averages, one of which improves a result by Sun and Zhou. At the end of this paper, as an example application of local average sampling, we consider a reconstruction algorithm: the piecewise linear approximations.