Two-dimensional nonuniform sampling expansions an iterative approach. ii. reconstruction formulae and applications
Two-dimensional nonuniform sampling expansions an iterative approach. ii. reconstruction formulae and applications
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二维非均匀采样扩展了一种迭代方法。
DOI：
10.1080/00036818908839839
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发表时间：
1989
影响因子：
1.1
通讯作者：
G. Hinsen
中科院分区：
文献类型：
--
作者：
P. Butzer;G. Hinsen
经典的采样定理指出，一个或两个变量的带限平方可积函数可以从它们在适当密集的等距节点集上采集的样本中重构。在一维中，均匀的采样点可以被某些不规则间隔的采样点代替。利用带限函数的性质和Nikol'skii不等式在[22]中的推广，建立了带限为以（0，0）为中心点的二维平方可积函数的非均匀采样定理。重建公式是由一元函数的抽样公式迭代应用而得。结果表明，所得到的系列绝对收敛，提供的采样点不是太广泛的分散。几个应用程序，包括六边形和椭圆形的采样点集。进一步的推广进行了讨论
The classical sampling theorems state that bandlimited square integrable functions of one or two variables can be reconstructed from their samples taken at suitably dense equally spaced sets of nodes. In one dimension, the uniform sampling points can be replaced by certain irregularly spaced ones. By making use of the properties of bandlimited functions and a generalization of an inequality of Nikol'skii shown in [22], in this part a nonuniform sampling theorem for two-dimensional square integrable functions bandlimited to a parallelogram centered at (0,0) is established. The reconstruction formula is obtained by iterative application of sampling formulae for functions of one variable. It is shown that the resulting series converges absolutely provided the sampling points are not too wildly scattered. Several applications are worked out, including those for hexagonal and octogonal sets of sampling points. Further generalizations are discussed