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

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