Stability Analysis for Autoregressive Sampling Sets

2026-06-02

AI Summary

This study investigates whether sampling sets generated by first-order autoregressive (AR(1)) modeled ADC clock jitter constitute stable sampling sets for Paley–Wiener signals. By integrating stochastic process modeling, classical sampling theory, matrix condition number analysis, and probabilistic stability arguments, the work demonstrates that although such sampling sets satisfy the asymptotic density required by the Nyquist–Shannon criterion, they almost surely lead to ill-posed infinite-dimensional reconstruction. In contrast, in finite-dimensional settings, the associated sinc interpolation matrices are shown to be well-conditioned with high probability. This paper provides the first rigorous theoretical characterization of the dual stability nature of AR(1) jittered sampling, clarifying that asymptotic density alone is insufficient for stable reconstruction and establishing probabilistic guarantees for favorable conditioning in finite dimensions.

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.

Problem

• stability
• sampling sets
• AR(1) jitter
• Paley-Wiener signals
• density

Innovation

• AR(1) jitter
• stable sampling
• Paley-Wiener space
• sinc matrix conditioning
• stochastic sampling