Powell, Alexander M.; Tanner, Jared; Wang, Yang; Yılmaz, Özgür Coarse quantization for random interleaved sampling of bandlimited signals. (English) Zbl 1314.94037 ESAIM, Math. Model. Numer. Anal. 46, No. 3, 605-618 (2012). Summary: The compatibility of unsynchronized interleaved uniform sampling with Sigma-Delta analog-to-digital conversion is investigated. Let \(f\) be a bandlimited signal that is sampled on a collection of \(N\) interleaved grids \(\{kT + T_n\}_{k\in \mathbb {Z}}\) with offsets \(\{T_n\}^N_{n=1}\subset[0,T]\). If the offsets \(T_n\) are chosen independently and uniformly at random from \([0,T]\) and if the sample values of \(f\) are quantized with a first order Sigma-Delta algorithm, then with high probability the quantization error \(|f(t) - \widetilde{f}(t)|\) is at most of order \(N^{-1}\log N\). Cited in 2 Documents MSC: 94A20 Sampling theory in information and communication theory 41A30 Approximation by other special function classes 94A12 Signal theory (characterization, reconstruction, filtering, etc.) Keywords:analog-to-digital conversion; bandlimited signals; interleaved sampling; random sampling; sampling expansions; sigma-delta quantization PDFBibTeX XMLCite \textit{A. M. Powell} et al., ESAIM, Math. Model. Numer. Anal. 46, No. 3, 605--618 (2012; Zbl 1314.94037) Full Text: DOI