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 collection of N interleaved grids {kT + T-n}(k is an element of Z) with offsets {T-n}(n=1)(N) subset of [0, T]. If the offsets T-n 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 vertical bar f(t) - (f) over tilde (t)vertical bar is at most of order N-1 log N.