Approximating Non-band-limited Functions by Nonuniform Sampling Series
Approximating Non-band-limited Functions by Nonuniform Sampling Series
复制标题
通过非均匀采样级数逼近非带限函数
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
P. Ferreira
中科院分区：
文献类型：
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作者：
P. Ferreira
本文提出了一种用有限个非均匀采样序列逼近一类非带限函数的新方法。该方法基于一个简单的想法：用有限和逼近卷积积分，然后使用有限和来获得逼近误差的上限。采样序列不必基于通常的sin（wt）=（t）核，并且它们的收敛性可以在不诉诸迭代方法的情况下建立。证明是完全基于\真实的变量”，基本参数。本文的主要目的是证明一系列的N项，这是O（w logw）=N的通常的核，是O（w）=N的某些其他核的逼近误差。
We describe a new method of approximating a class of non-band-limited functions by nite nonuniform sampling series. The method is based on a simple idea: that of approximating a convolution integral by a nite sum, and then using the nite sum to obtain an upper bound for the approximation error. The sampling series do not have to be based on the usual sin(wt)=(t) kernel, and their convergence can be established without resorting to iterative methods. The proofs are entirely based on \real variable", elementary arguments. The main purpose of this paper is to show that the approximation error for a series of N terms, which is O(w logw)=N for the usual kernel, is O(w)=N for certain other kernels.