RECONSTRUCTION OF OVERSAMPLED BAND-LIMITED SIGNALS FROM SIGMA-DELTA ENCODED BINARY SEQUENCES

We consider the application of SIGMADELTA modulators to analog-to-digi tal conversion. We have previously shown that for constant input signa ls, optimal nonlinear decoding can achieve large gains in signal-to-no ise ratio (SNR) over linear decoding. In this paper we show a similar result for band-limited input signals. The new nonlinear decoding algo rithm 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 quadrati c programming problem. The band limitation can be based on singular va lue decomposition of a certain matrix. We show simulation results for the SNR performance of a POCS-based decoder and a linear decoder for t he single loop, double loop and two-stage SIGMADELTA modulators and fo r a specific fourth-order interpolative modulator. Depending on the mo dulator and the oversampling ratio, improvements in SNR of up to 10-20 dB can be achieved.