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arXiv · 2011.12877

Error estimates in Second-order Continuous-Time Sigma-Delta modulators

Dilshad Surroop·Pascal Combes·Philippe Martin
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Abstract

Continuous-time Sigma-Delta (CT-$\Sigma\Delta$) modulators are oversampling Analog-to-Digital converters that may provide higher sampling rates and lower power consumption than their discrete counterpart. Whereas approximation errors are established for high-order discrete time $\Sigma\Delta$ modulators, theoretical analysis of the error between the filtered output and the input remain scarce. This paper presents a general framework to study this error: under regularity assumptions on the input and the filtering kernel, we prove for a second-order CT-$\Sigma\Delta$ that the error estimate may be in $o(1/N^2)$, where $N$ is the oversampling ratio. The whole theory is validated by numerical experiments.

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Dilshad Surroop, Pascal Combes, Philippe Martin. 2020-11-25. Error estimates in Second-order Continuous-Time Sigma-Delta modulators. https://arxiv.org/abs/2011.12877

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