Sigma delta modulation of a chaotic time series: a non-linear signal in a non-linear system

Abstract

Sigma delta modulators are a form of analogue to digital converter used in a broad range of signal processing environments. There has been speculation recently that such devices may be capable of chaotic modes of operation. The first section of this paper examines this possibility. There is also a greater concern that, due to the non-linear nature of these devices, sigma-delta modulation of a chaotic signal may affect the long-term predictability of that signal. This is examined by considering a range of invariant geometric properties of a signal before and after sigma delta modulation, including the Lyapunov exponents and the correlation dimension. It is shown that, although the sigma delta modulator is not in itself a chaotic system, it can affect these geometric properties and therefore the predictability of the signal being measured.<>