Mathematical Analysis of ΣΔ Modulators and Applications on Frequency Synthesis and Stochastic Filtering
Anastasios Vlachos
Abstract
The main goal of this thesis is the mathematical analysis of SD modulators and the presentation of two fields where they can be applied to: the field of frequency synthesis and the field of digital stochastic filtering. Firstly, we study SD modulators with constant inputs from the scope of piecewise continuous mappings and we draw conclusions about their periodicity. Furthermore, we show how SD modulators can be used in applications of frequency synthesis and we present techniques in order to maximize their periodicity, so that they can be used optimally in frequency synthesis applications. Finally, we present a digital signal processing scheme, that is based on SD modulators and Stochastic Computing techniques, and we present the benefits of the combinations of these two methods. All theoretical results of this thesis are accompanied by simulation results that were carried out using Matlab.