Asymptotic MSE law of nth-order (sigma)(delta) modulators

The mean squared error (MSE) of an nth-order (sigma)(delta) modulator is classically understood to decay with the oversampling ratio M at the rate (alpha)/M/sup 2n+1/. In this paper, we demonstrate by experimental evidence and basic analytical explanations that the accurate general MSE law is in fact in ((beta)/M/sup 2n/)+((gamma)/M/sup 2n+1/) instead. The coefficient (beta) is in general not zero, except when the input is rigorously constant, or when using the ideal standard nonoverloaded n-bit n-loop modulator. The term (beta)/M/sup 2n/ is dominant starting from low values of M when using a one-bit quantizer.