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Continuous-time Sigma-Delta (CT-$\Sigma\Delta$) modulators are oversamplingAnalog-to-Digital converters that may provide higher sampling rates and lowerpower consumption than their discrete counterpart. Whereas approximation errorsare established for high-order discrete time $\Sigma\Delta$ modulators,theoretical analysis of the error between the filtered output and the inputremain scarce. This paper presents a general framework to study this error:under regularity assumptions on the input and the filtering kernel, we provefor 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 validatedby numerical experiments.

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