DETERMINISTIC ANALYSIS OF OVERSAMPLED A D CONVERSION AND DECODING IMPROVEMENT BASED ON CONSISTENT ESTIMATES/

This paper deals with the deterministic analysis of oversampled A/D co nversion (ADC), the properties derivable from such an analysis, and th e consequences on reconstruction using nonlinear decoding. Given a ban dlimited input X producing a quantized version C, we consider the set of all input signals that are bandlimited and produce C. We call any e lement of this set a consistent estimate of X. Regardless of the type of encoder (simple, predictive, or noise-shaping), we show that this s et is convex, and as a consequence, any nonconsistent estimate can be improved. We also show that the classical linear decoding estimates ar e not necessarily consistent. Numerical tests performed on simple ADC, single-loop, and multiloop SIGMADELTA modulation show that consistent estimates yield an MSE that decreases asymptotically with the oversam pling ratio faster than the linear decoding MSE by approximately 3 dB/ octave. This implies an asymptotic MSE of the order of O(R-(2n+2)) ins tead of O(R-(2n+1)) in linear decoding, where R is the oversampling ra tio and n the order of the modulator. Methods of improvements of nonco nsistent estimates based on the deterministic knowledge of the quantiz ed signal are proposed for simple ADC, predictive ADC, single-loop, an d multiloop SIGMADELTA modulation.