Approximation from shift-invariant spaces by generalized sampling formulas
Approximation from shift-invariant spaces by generalized sampling formulas
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DOI：
10.1016/j.acha.2007.06.002
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发表时间：
2008
影响因子：
2.5
通讯作者：
Antonio G. García;G. Pérez-Villalón
中科院分区：
文献类型：
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作者：
Antonio G. García;G. Pérez-Villalón
本文利用广义采样公式研究了平移不变空间的逼近问题。这些采样公式涉及函数本身的过滤版本的样本。所考虑的系统包括平均采样器，和经典的函数及其衍生物的采样。在对移位不变空间的生成元φ和所涉及的系统作适当的假设下，我们得到了Lp（Rn）的移位不变子空间中稳定的广义采样公式.从这些广义采样公式，我们构造逼近方案有效的光滑函数。近似阶取决于φ满足Strang-Fix条件的阶数，以及系统中出现的导数的最大阶数。
In this paper we investigate approximation from shift-invariant spaces by using generalized sampling formulas. These sampling formulas involve samples of filtered versions of the function itself. The considered systems include averaging samplers, and classical sampling of the function and its derivatives. Under appropriate hypotheses on the generator φ of the shift-invariant space and on the involved systems, we derive stable generalized sampling formulas in a shift-invariant subspace of Lp(Rn). From these generalized sampling formulas we construct approximation schemes valid for smooth functions. The approximation order depends both on the order for which the Strang–Fix conditions are satisfied by φ, and on the largest order of the derivatives appearing in the systems if any.