Geodesic
Coarse quantization for random interleaved sampling of bandlimited signals
ESAIM: Mathematical Modelling and Numerical Analysis , Special volume in honor of Professor David Gottlieb. Numéro spécial, Tome 46 (2012) no. 3, pp. 605-618

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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]} { 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)|} | f ( t ) - 􏽥 f ( t ) | is at most of order N-1log N.

DOI : 10.1051/m2an/2011057
Classification : 41A30, 94A12, 94A20
Keywords: 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://geodesic.mathdoc.fr/articles/10.1051/m2an/2011057/}
}
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Powell, Alexander M.; Tanner, Jared; Wang, Yang; Yılmaz, Özgür. Coarse quantization for random interleaved sampling of bandlimited signals. ESAIM: Mathematical Modelling and Numerical Analysis , Special volume in honor of Professor David Gottlieb. Numéro spécial, Tome 46 (2012) no. 3, pp. 605-618. doi: 10.1051/m2an/2011057

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