Motivated by recent developments in stochastic modeling of clock jitter in Analog-to-Digital Converters (ADCs) as autoregressive processes of order one (AR(1)), we study the density and stability properties of AR(1)-jittered sampling sets for Paley-Wiener signals. We show that, despite having the correct asymptotic density both on average and almost surely, such sets almost surely fail to be stable sampling sets. We complement this negative result with a finite-dimensional analysis, showing that the corresponding jittered sinc matrices are nonetheless well-conditioned with high probability.

翻译：受模拟-数字转换器（ADC）中时钟抖动被建模为一阶自回归过程（AR(1)）这一最新进展的启发，我们研究了Paley-Wiener信号在AR(1)抖动采样集下的密度与稳定性性质。我们证明，尽管这类采样集在平均意义和几乎必然意义下均具有正确的渐近密度，但它们几乎必然无法构成稳定采样集。我们通过有限维分析补充了这一负面结论，表明相应的抖动sinc矩阵仍以高概率保持良好的条件数。