Reconstruction of oversampled band-limited signals from Sigma Delta encoded binary sequences

The application of Sigma Delta modulators to analog-to-digital conversion is examined, with attention given to the case of bandlimited input signals. The novel nonlinear decoding scheme considered here is based on the theory of projections onto convex sets (POCS), and alternates between a bandlimiting operation and a time-domain operation to find a signal invariant under both. For general bandlimited inputs, the band limitation can be based on singular value decomposition of a certain matrix. The time-domain operation results in a quadratic programming problem. The authors show simulation results for the SNR (signal-to-noise ratio) performance of a POCS-based decoder for the single-loop Sigma Delta modulator and a specific fourth-order interpolative modulator, and present comparisons with linear decoding. Improvements in SNR of up to 20-30 dB can be achieved for the single-loop modulator, and up to 10-15 dB for the fourth-order modulator.<<ETX>>