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：受模数转换器（ADC）中时钟抖动的随机建模（即一阶自回归过程（AR(1)））最新进展的启发，我们研究了Paley-Wiener信号在AR(1)抖动采样集合下的密度与稳定性性质。结果表明，尽管此类集合在平均意义和几乎必然意义下均具有正确的渐进密度，但它们几乎必然无法构成稳定的采样集合。我们通过有限维分析补充了这一负面结论：尽管存在上述缺陷，相应的抖动sinc矩阵仍以高概率保持良态条件数。