Granular quantization noise in a class of delta-sigma modulators

The trend toward digital signal processing in communication systems has resulted in a large demand for fast accurate analog-to-digital (A/D) converters, and advances in VLSI technology have made ΔΣ modulator-based A/D converters attractive solutions. However, rigorous theoretical analyses have only been performed for the simplest ΔΣ modulator architectures. Existing analyses of more complicated ΔΣ modulators usually rely on approximations and computer simulations. In the paper, a rigorous analysis of the granular quantization noise in a general class of ΔΣ modulators is developed. Under the assumption that some input-referred circuit noise or dither is present, the second-order asymptotic statistics of the granular quantization noise sequences are determined and ergodic properties are derived