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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 ∈ Zwith offsets T n n = 1 N ⊂ [ 0 ,T ] . If the offsetsTn are chosen independently and uniformly at random from [0,T] and if the sample values of fare quantized with a first order Sigma-Delta algorithm, then with high probability the quantization error | f ( t ) − x10ff65;...
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 . 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...
Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.
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