Reconstruction of oversampled signals from the solution space of delta-sigma modulated sequences

In this paper, we investigate non-linear methods for reconstruction of oversampled signals from the single-bit delta-sigma (ΔΣ) modulated sequences. We consider the scenario where the output sequence defines the solution space of input signals but not the initial signal estimate. We show that for a sufficiently large oversampling ratio (OSR), any point in the solution space can be taken as a signal estimate and that the reconstruction procedure becomes a solver for a linear feasibility problem. In addition, we show that the reconstruction process can be designed in the time domain and we illustrate how removing edge constraints from the block decoder can be used to find a feasible solution and reduce the dimension of the problem. The simulation results in this setting show that our method is up to three times faster than the direct projection (DP) method.