Reduction of the MSE in R-times oversampled A/D conversion from O(1/R) to O(1/R^2)

In oversampled analog-to-digital conversion, the usual reconstruction method using lowpass filtering leads to a mean squared error (MSE) inversely proportional to the oversampling ratio R. The authors prove, under certain assumptions and with periodic analog input signals, that optimal reconstruction achieves an MSE with an oversampling ratio dependence order of at least O(1/R2). That is, an MSE slope of -6 dB per octave of oversampling is obtained, rather than the conventional -3 dB/octave slope of classical schemes