BOUNDEDNESS AND APERIODICITY OF COMMERCIAL SIGMA DELTA MODULATORS

Sigma delta modulation is a popular form of A/D and D/A conversion. This nonlinear device exhibits a high degree of complex nonlinear behaviour, including chaotic dynamics. One of the main unsolved problems in the theory of sigma delta modulation concerns the ability to analytically derive conditions for the boundedness of solutions of a high order sigma delta modulator (SDM). In this work, we describe how a sigma delta modulator may be rephrased within the context of systems theory. We present several theoretical results concerning bounded solutions of general high order SDMs, including necessary and sufficient conditions for the lack of a finite escape time, necessary conditions for bounded solutions based on the nature of the output sequences, and topological properties of the solutions, which are a precursor to the study of chaotic solutions of SDMs.