Coarse quantization for random interleaved sampling of bandlimited signals

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 col- lection of N interleaved grids {kT + Tn}k∈Z with offsets {Tn} N=1 ⊂ (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 |f (t) − � f (t)| is at most of order N −1 log N.

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