ERROR ESTIMATES IN SECOND-ORDER CONTINUOUS-TIME SIGMA-DELTA MODULATORS

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.