Stability Analysis for Autoregressive Sampling Sets
2026-06-02 • Information Theory
Information Theory
AI summaryⓘ
The authors study how small timing errors, modeled as a specific type of random process called AR(1), affect the sampling of certain types of signals known as Paley-Wiener signals. They find that although these timing errors keep the average sampling density correct, the samples are almost never stable enough for perfect signal reconstruction. However, when looking at smaller, finite cases, the related mathematical matrices remain well-behaved with high probability. This suggests that while large-scale stability is lost, practical finite scenarios might still be manageable.
Analog-to-Digital Converters (ADCs)clock jitterautoregressive process AR(1)sampling densityPaley-Wiener signalsstable sampling setssinc matricesmatrix conditioning
Authors
Daniele Gerosa, Thomas Eriksson
Abstract
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.