Mixed continuous/discrete time modelling with exact time adjustments

Many systems interact with their physical environment. Design of such systems need a modelling and simulation tool which can deal with both the continuous and discrete aspects. However, most current tools are not adequately able to do so, as they implement both continuous and discrete time signals as consisting of separate values at a single global simulation clock. The consequence is that simulation, of a time delay for example, either yields inaccurate results or becomes inefficient. We propose a solution by considering (continuous) signals as functions of time and by separating different notions of time. Signals thus correspond directly to their mathematical representation and e.g. time delays can be dealt with exactly. A second advantage is that discretisation of time can be dealt with locally, such that numerical approximations in the continuous time domain or sampling of the ADC can be calculated without influencing the time granularity of the rest of the system. To handle such signals, we need higher order functions. As they are standard in functional languages, we implement our approach in Haskell. We illustrate the approach with a case study on beamforming in phased array systems.