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 + Tn} k ∈ Z with offsets \hbox{} { T n } n = 1 N ⊂ [ 0 ,T ] . If the offsets Tn 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 ) - 􏽥 f ( t ) | is at most of order N-1log N.
Mots clés : analog-to-digital conversion, bandlimited signals, interleaved sampling, random sampling, sampling expansions, sigma-delta quantization
@article{M2AN_2012__46_3_605_0, author = {Powell, Alexander M. and Tanner, Jared and Wang, Yang and Y{\i}lmaz, \"Ozg\"ur}, title = {Coarse quantization for random interleaved sampling of bandlimited signals}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {605--618}, publisher = {EDP-Sciences}, volume = {46}, number = {3}, year = {2012}, doi = {10.1051/m2an/2011057}, mrnumber = {2877367}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2011057/} }
TY - JOUR AU - Powell, Alexander M. AU - Tanner, Jared AU - Wang, Yang AU - Yılmaz, Özgür TI - Coarse quantization for random interleaved sampling of bandlimited signals JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2012 SP - 605 EP - 618 VL - 46 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2011057/ DO - 10.1051/m2an/2011057 LA - en ID - M2AN_2012__46_3_605_0 ER -
%0 Journal Article %A Powell, Alexander M. %A Tanner, Jared %A Wang, Yang %A Yılmaz, Özgür %T Coarse quantization for random interleaved sampling of bandlimited signals %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 605-618 %V 46 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2011057/ %R 10.1051/m2an/2011057 %G en %F M2AN_2012__46_3_605_0
Powell, Alexander M.; Tanner, Jared; Wang, Yang; Yılmaz, Özgür. Coarse quantization for random interleaved sampling of bandlimited signals. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 3, pp. 605-618. doi : 10.1051/m2an/2011057. http://www.numdam.org/articles/10.1051/m2an/2011057/
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