One-Bit Sigma-Delta Modulation on a Closed Loop

In this paper, we propose a scheme for the first order one-bit ΣΔ modulation on a closed loop. In contrast to schemes designed for the real line, which rely entirely on a recurrence relation, the difficulty of this setting is to avoid mismatches at the initialization point. In order to distribute the error equally around the loop, we propose an update of the samples using information we gain from the classical approach. We prove that the proposed scheme leads to a smaller reconstruction error and we discuss how this scheme can be extended to higher orders.