Breaking the feedback loop of ΣΔ modulators

Although the topic of analog-to-digital (A/D) conversion should fundamentally be part of the signal processing area, paradoxically, very little signal theory has been devoted to it. One reason is that the main technique currently used in data acquisition, called ΣΔ modulation, consists of coarse quantization with feedback. This prevents the normal resolution of the output of the system in terms of its input, contrary to the case of linear feedback systems. The paper introduces new tools to solve this problem and enable rigorous signal error analysis of ΣΔ modulators.