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An Improved Nyquist–Shannon Irregular Sampling Theorem From Local Averages

机译：基于局部平均值的改进的Nyquist–Shannon不规则采样定理

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摘要

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.
机译：奈奎斯特-香农采样定理是根据其均匀采样的样本重建带限信号。信号带宽越高，统一采样的难度就越大。为了解决这个问题，在文献中已经研究了从局部平均值重建信号。在本文中，我们从一般局部平均数中获得了改进的Nyquist–Shannon采样定理。在实践中，测量设备在不对称间隔内给出加权平均值。作为一种特殊情况，对于对称间隔的局部平均值，我们表明采样率远低于Gröchenig的结果。此外，我们从局部平均值中获得了两个精确的双帧，其中之一提高了Sun和Zhou的结果。在本文的最后，作为局部平均采样的示例应用，我们考虑一种重构算法：分段线性逼近。

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