Sampling and Reconstruction of Operators
Sampling and Reconstruction of Operators
复制标题
算子采样与重构
DOI：
10.1109/tit.2015.2501646
复制
发表时间：
2015
影响因子：
2.5
通讯作者：
D. Walnut
中科院分区：
文献类型：
--
作者：
G. Pfander;D. Walnut
我们研究了恢复运营商的带限科恩-尼伦伯格符号的行动，这样的运营商的加权脉冲序列，一个程序，我们称之为采样的运营商。Kailath，Bello，后来Kozek和作者已经证明，如果算子的符号被带限为面积小于1的集合，则算子的采样是可能的。在本文中，我们发展的理论采样的运营商类似的经典理论采样的带限函数。定义了算子的采样集和采样率的概念，给出了采样率依赖于带限集的大小和几何形状的充要条件。我们开发了显式重建公式的运营商采样，推广重建公式的带限函数。我们给必要和充分条件的bandlimiting集下，采样的运营商是可能的，由他们的行动对一个给定的周期性加权三角火车。我们表明，在温和的几何条件下的bandlimiting集，类的运营商bandlimited到一个未知的一组面积小于一半允许采样和重建。我们推广了两个结果的海克尔和Bo lclcskei关于采样的运营商的面积不大于一半，小于1，分别通过寻找一个更大的类的运营商，他们适用。具有带限符号的算子已经被用来模拟具有慢时变脉冲响应的双色散通信信道。本文的结果是植根于工作的贝洛和Kailath在20世纪60年代。
We study the recovery of operators with a bandlimited Kohn-Nirenberg symbol from the action of such operators on a weighted impulse train, a procedure we refer to as sampling of operators. Kailath, Bello, and later Kozek and the authors have shown that the sampling of operators is possible if the symbol of the operator is bandlimited to a set with area less than one. In this paper, we develop the theory of the sampling of operators in analogy with the classical theory of sampling of bandlimited functions. We define the notions of sampling set and sampling rate for operators and give necessary and sufficient conditions on the sampling rate that depend on the size and geometry of the bandlimiting set. We develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions. We give necessary and sufficient conditions on the bandlimiting set under which sampling of operators is possible by their action on a given periodically weighted delta train. We show that under mild geometric conditions on the bandlimiting set, classes of operators are bandlimited to an unknown set of area less than one-half permit sampling and reconstruction. We generalize two results of the Heckel and Bölcskei concerning sampling of operators with area not greater than one-half and less than one, respectively, by finding a larger class of operators to which they apply. Operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly time-varying impulse response. The results in this paper are rooted in work by Bello and Kailath in the 1960s.
运营商抽样
影响因子：
1.2
作者：
G. E. Pfander.
通讯作者：
G. E. Pfander.
影响因子：
2.5
作者：
F. Krahmer;G. Pfander;Peter Rashkov
通讯作者：
F. Krahmer;G. Pfander;Peter Rashkov
DOI：
10.1016/j.acha.2013.05.001
发表时间：
2014
期刊：
ArXiv
影响因子：
--
作者：
G. E. Pfander;P. Zheltov
通讯作者：
P. Zheltov