频率局部化信号的广义采样定理
A Generalized Sampling Theorem for Frequency Localized Signals
摘要：
本文提出了频率局部化信号的一个广义采样定理。所提出的采样模型的推广是双重的：（1）它适用于各种预滤波器，实现“软”带限，（2）从样本值获得近似重建，而不是完美的（尽管前者在许多情况下可能是“实际上完美的”）。对于任意的有限能量信号的频率局部化是由一个预滤波器实现与规定的属性的函数的互相关。滤波器的范围，即所谓的局部化空间，被详细描述。采用规则采样法，给出了重建公式。对于重建误差的一般误差估计推导出一个关键的采样间隔和“软带宽”的预滤波器的概念之间的连接表示。基于正弦函数，高斯函数和B样条的例子进行了讨论。
英文摘要：
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate reconstruction from sample values rather than a perfect one is obtained (though the former might be "practically perfect" in many cases). For an arbitrary finite-energy signal the frequency localization is performed by a prefilter realizing a crosscorrelation with a function of prescribed properties. The range of the filter, the so-called localization space, is described in some detail. Regular sampling is applied and a reconstruction formula is given. For the reconstruction error a general error estimate is derived and connections between a critical sampling interval and notions of "soft bandwidth" for the prefilter are indicated. Examples based on the sinc-function, Gaussian functions and B-splines are discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
