NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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 [...] modulator based A/D converters attractive solutions. However, because they are non-linear systems, they have proven difficult to analyze. Rigorous analyses have been previously performed only for a small number of artificial input sequences and then only for the simplest of [...] modulator architectures. This thesis consists of three self-contained papers addressing these and related problems. The first two papers extend the repertoire of tractable input sequences for most of the known DE modulator architectures. The third paper applies the results from the first two papers to develop a scalable architecture for parallel [...] Modulation. The first paper concentrates on the first-order [...] modulator and develops rigorous results for a large class of input sequences. Under the assumptions that some circuit noise is present and that the input sequence does not cause overload, a simple autocorrelation expression is developed that is only locally dependent upon the input sequence. Ergodic properties are derived and various examples are presented. In the second paper, a rigorous analysis of the granular quantization noise in a general class of DE modulators is developed. Again under the assumption that some circuit noise is present, the joint statistics of the granular quantization noise sequences are determined and the sequences are shown to be correlation ergodic. The exact results developed for the granular quantization noise are shown to approximately hold for the overall quantization noise if the quantizers in the [...] modulator overload occasionally. The third paper develops a scalable A/D converter architecture consisting of multiple [...] modulators. By combining [...] modulator based A/D converters, each with an oversampling ratio of N, an effective oversampling ratio of approximately NM is achieved with only an M-fold increase in the quantization noise power. In particular, the special case of N = 1 allows for full-rate analog to digital conversion. Unlike most other approaches to trading modulator complexity for accuracy, the system retains the robustness of the individual [...] modulators to circuit imperfections.