This research project attempts to apply nonlinear dynamical systems theory to sigma-delta modulators nonlinear systems whose increasingly widespread use in signal conversion is unfortunately not matched by a rigorous theoretical foundation. Most analyses of sigma-delta modulators rely on linearising assumptions and cannot explain such important practical effects as oscillations, multiplicity of solutions and instability In my Ph.D.studies I examined such effects in a related system (DPCM, which like sigma-delta modulation is modelled by a noninvertible piecewise-continuous map) with the aid of theories of nonlinear dynanmics and in particular those of noninvertible maps. I now propose to extend this work to develop an improved theoretical understanding firstly of sigma-delta modulation, and more generally of noninvertible piecewise- continuous discrete-time dynamics in electronic systems.
Training content (objective, benefit and expected impact)
I will extend and capitalise on my existing background to develop an expertise in practical and theoretical aspects of electronic systems which are of huge importance to industry, with the important benefit of industrial contact throughout my research.
Links with industry / industrial relevance (22)
The host group is partially funded by Analog Devices, one of the leading manufacturers of sigma-delta modulators, for research in this area, affording me the possibility of direct and valuable contact with industry concerning my research.