Stability Analysis for Autoregressive Sampling Sets
This work addresses the stability of non-uniform sampling arising from clock jitter in ADCs, providing a negative theoretical result but a positive finite-dimensional counterpart.
The paper shows that AR(1)-jittered sampling sets for Paley-Wiener signals almost surely fail to be stable, despite having correct asymptotic density. However, the corresponding jittered sinc matrices are well-conditioned with high probability.
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.