A deterministic analysis of oversampled A/D conversion and Sigma Delta modulation

As an alternative to the usual statistical analysis, the authors present a purely deterministic analysis of oversampled A/D (analog-to-digital) conversion and sigma-delta modulation, which requires no assumption on the quantizer error. This leads to the notion of a consistent estimate for the decoding, which is a necessary condition for optimality. Algorithms using convex projections are discussed and the reduction of decoding error from SiO(R/sup -(2n+1)/)to SiO(SiR/sup -(2n+2)/) (where R is the oversampling ratio and n is the order of the encoder) is demonstrated experimentally for multiloop and multistage sigma-delta modulators.<>