Reconstruction of oversampled band-limited signals from ΣΔ encoded binary sequences

Considers the application of ΣΔ modulators to analog-to-digital conversion. The authors have previously shown that for constant input signals, optimal nonlinear decoding can achieve large gains in signal-to-noise ratio (SNR) over linear decoding. The present paper shows a similar result for band-limited input signals. The new nonlinear decoding algorithm is based on projections onto convex sets (POCS), and alternates between a time-domain operation and a band limitation to find a signal invariant under both. The time-domain operation results in a quadratic programming problem. The band limitation can be based on singular value decomposition of a certain matrix. The authors show simulation results for the SNR performance of a POCS-based decoder and a linear decoder for the single loop, double loop and two-stage ΣΔ modulators and for a specific fourth-order interpolative modulator. Depending on the modulator and the oversampling ratio, improvements in SNR of up to 10-20 dB can be achieved