We investigate the Gibbs–Wilbraham phenomenon for generalized sampling series, and related interpolation series arising from cardinal functions. We prove the existence of the overshoot characteristic of the phenomenon for certain cardinal functions, and characterize the existence of an overshoot for sampling series.

中文翻译：

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关于采样和插值级数的 Gibbs-Wilbraham 现象

我们研究了广义采样序列的 Gibbs-Wilbraham 现象，以及由基函数产生的相关插值序列。我们证明了某些基函数现象的过冲特征的存在，并表征了采样序列的过冲的存在。