On the relationship between splines, sampling zeros and numerical integration in sampled-data models for linear systems

Real systems are usually modelled in continuous-time by differential equations but, in practice, we have to deal with them through digital devices using sampled data. For linear systems, exact sampled-data models can be obtained. These models, however, will generally have more zeros than the continuous-time model. In this paper we show that there is a specific relation between the characterization of these sampling zeros and the order of the B-splines used to generate the continuous-time input to the system. Moreover, we show that this connection can also be established if the smoothness of the B-spline is taken into account in the integration strategy used to discretize the continuous-time model.