Oversampling in Shift-Invariant Spaces With a Rational Sampling Period
Oversampling in Shift-Invariant Spaces With a Rational Sampling Period
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DOI：
10.1109/tsp.2009.2021497
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发表时间：
2009-09
影响因子：
5.4
通讯作者：
Antonio G. García;M. A. Hernández-Medina;G. Pérez-Villalón
中科院分区：
文献类型：
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作者：
Antonio G. García;M. A. Hernández-Medina;G. Pérez-Villalón
众所周知，在适当的假设下，采样公式允许我们从采样周期为1的采样中恢复主移位不变空间中的任何函数。当移位不变空间的生成元满足r阶Strang-Fix条件时，这个公式也提供了一个对光滑函数有效的r阶逼近方案。本文利用小于1的有理采样周期，得到了具有相同特征的采样公式。使用这种过采样技术后，采样公式不是一个而是无限多个。只要生成元有紧支集，在这些公式中就有可能找到一个其相关重构函数也有紧支集的公式。
It is well known that, under appropriate hypotheses, a sampling formula allows us to recover any function in a principal shift-invariant space from its samples taken with sampling period one. Whenever the generator of the shift-invariant space satisfies the Strang-Fix conditions of order r, this formula also provides an approximation scheme of order r valid for smooth functions. In this paper we obtain sampling formulas sharing the same features by using a rational sampling period less than one. With the use of this oversampling technique, there is not one but an infinite number of sampling formulas. Whenever the generator has compact support, among these formulas it is possible to find one whose associated reconstruction functions have also compact support.