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We investigate the Gibbs–Wilbraham phenomenon for generalized sampling series, and related interpolation series arising from cardinal functions. We prove the existence of the overshoot characteristic of the phenomenon for certain cardinal functions, and characterize the existence of an overshoot for sampling series.

The compatibility of unsynchronized interleaved uniform sampling with Sigma-Deltaanalog-to-digital conversion is investigated. Let f be a bandlimitedsignal that is sampled on a collection of N interleaved grids {kT + Tn} k ∈ Zwith offsets \hbox{$\{T_n\}_{n=1}^N\subset [0,T]$} ${T_{n}}_{n = 1}^{N} \subset [0,T]$ . If the offsets Tn arechosen independently and uniformly at random from [0,T] and if thesample values of f are quantized with a first order Sigma-Deltaalgorithm, then with high probability the quantization error \hbox{$|f(t) - \widetilde{f}(t)|$} $| f (t) - \begin{matrix} _{􏽥} \\ f \end{matrix} (t) |$ is at most of orderN-1log N.

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On the Gibbs–Wilbraham Phenomenon for Sampling and Interpolatory Series

Coarse quantization for random interleaved sampling ofbandlimited signals ∗∗∗

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On the Gibbs–Wilbraham Phenomenon for Sampling and Interpolatory Series

Coarse quantization for random interleaved sampling ofbandlimited signals∗∗∗

Coarse quantization for random interleaved sampling ofbandlimited signals ∗∗∗