Deterministic analysis of oversampled A/D conversion and decoding improvement based on consistent estimates

is paper deals with the deterministic analysis of oversampled A/D conversion (ADC), the properties derivable from such an analysis, and the consequences on reconstruc- tion using nonlinear decoding. Given a bandlimited input X producing a quantized version C , we consider the set of all input signals that are bandlimited and produce C. We call any element of this set a consistent estimate of X. Regardless of the type of encoder (simple, predictive, or noise-shaping), we show that this set is convex, and as a consequence, any nonconsistent estimate can be improved. We also show that the classical linear decoding estimates are not necessarily consistent. Numerical tests performed on simple ADC, single-loop, and multiloop ΣΔ modulation show that consistent estimates yield an MSE that decreases asymptotically with the oversampling ratio faster than the linear decoding MSE by approximately 3 dB/octave. This implies an asym totic MSE of the order of O(R-('"+')) instead of O(R-(2"c'p)in linear decoding, where R is the oversampling ratio and n the order of the modulator. Methods of improvements of nonconsistent estimates based on the deterministic knowledge of the quantized signal are proposed for simple ADC, predictive ADC, single-loop, and multiloop ΣΔ modulation.