A new interpretation and extension of ΣΔ modulation

The conventional analysis and understanding of ΣΔ modulation is based on linear systems theory with some exceptions. The presence of a nonlinear element (quantizer) undermines the validity of the analysis when the underlying assumptions of input signal independence, whiteness and uniform distribution of quantization noise are suspect. The assumptions, in particular, have not been proved to be true for high order (>1) 1-bit modulators and there is empirical and/or analytical evidence to show that these assumptions are sometimes false. This paper presents a new result about noise-shaping in high order 1-bit ΣΔ modulation, and a new framework within which to view ΣΔ modulation. ΣΔ modulation is presented as an instance of a solution to an optimization problem. This view not only offers insight into the behavior of ΣΔ modulation but also suggests novel extensions