Coarse quantization for random interleaved sampling of bandlimited signals

Abstract

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 <inf>n</inf>} <inf>k Z</inf> with offsets \hbox{$\{T-n\}-{n=1}N\subset [0,T]$. If the offsets T<inf>n</inf> 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 \hbox{$|f(t) - \widetilde{f}(t)|$}is at most of order N^-1log N. © EDP Sciences, SMAI, 2012.