Error Estimates in Second-Order Continuous-Time Sigma-Delta Modulators

Continuous-time Sigma-Delta (CT-ΔΣ) 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 ΔΣ 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-ΔΣ 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.