Oversampling and Coarse Quantization for Signals

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Time Average MSE Analysis for Sigma-Delta Modulator

Dr. Bin Han

Mathematical and Statistical Sciences at University of Alberta

Abstract:   Based on experiment and numerical simulation, it has been widely believed that the time average mean square error (MSE) in the first order sigma-delta modulator with input of bandlimited signals decays likes O(\lambda^{-3}) as the sampling ratio \lambda goes to infinity. This conjecture remains as an open problem for many years. Combining tools from number theory, harmonic analysis, real analysis and complex analysis, building on several interesting works of Daubechies, DeVore and Güntürk, we will show that the conjecture holds in some reasonable sense for the first order sigma-delta modulator. The technique used here for the first order sigma-delta modulator is also applicable to higher order sigma-delta modulators.