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Coarse quantization for random interleaved sampling of bandlimited signals. (English) Zbl 1314.94037

Summary: 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 \(\{kT + T_n\}_{k\in \mathbb {Z}}\) with offsets \(\{T_n\}^N_{n=1}\subset[0,T]\). 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 \(|f(t) - \widetilde{f}(t)|\) is at most of order \(N^{-1}\log N\).

MSC:

94A20 Sampling theory in information and communication theory
41A30 Approximation by other special function classes
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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