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Coarse quantization for random interleaved sampling ofbandlimited signals∗∗∗

Published online by Cambridge University Press:  11 January 2012

Alexander M. Powell ,
Jared Tanner ,
Yang Wang  and
Özgür Yılmaz
Alexander M. Powell
Affiliation:
Department of Mathematics, Vanderbilt University, Nashville, 37240 TN, USA. alexander.m.powell@vanderbilt.edu
Jared Tanner
Affiliation:
School of Mathematics, University of Edinburgh, King’s Buildings, Mayfield Road, EH9 3JL Edinburgh, UK; jared.tanner@ed.ac.uk
Yang Wang
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, 48824 MI, USA; ywang@math.msu.edu
Özgür Yılmaz
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver B.C., V6T 1Z2 Canada; oyilmaz@math.ubc.ca
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Abstract

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Deltaanalog-to-digital conversion is investigated. Let f be a bandlimitedsignal that is sampled on a collection of N interleaved grids {kT + Tn} k ∈ Zwith offsets \hbox{$\{T_n\}_{n=1}^N\subset [0,T]$}{Tn}n=1N⊂[0,T]. If the offsets Tn arechosen independently and uniformly at random from  [0,T]  and if thesample values of f are quantized with a first order Sigma-Deltaalgorithm, then with high probability the quantization error \hbox{$|f(t) - \widetilde{f}(t)|$}|f(t)−􏽥f(t)|is at most of orderN-1log N.

Keywords

Analog-to-digital conversionbandlimited signalsinterleaved samplingrandom samplingsampling expansionsSigma-Delta quantization

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