Statistics of the Quantization Noise in 1-Bit Dithered Single-Quantizer Digital Delta–Sigma Modulators

An analysis of the quantization noise introduced by a widely-used class of single-quantizer digital delta-sigma (DeltaSigma) modulators with low-level, 1-bit dither is presented. Necessary and sufficient conditions are derived that ensure, in an asymptotic sense, various ensemble statistical properties of the quantization noise such as uniformity and independence from the input and delayed versions of itself. The conditions are also shown to be sufficient for a single realization of the quantization noise sequence to possess these properties in a time-averaged sense. Several of the most commonly-used digital DeltaSigma modulators are shown to satisfy the conditions