Reconstruction of continuous-time systems from their discretizations

The so-called zero-order hold discretization or step-invariant transformation is not one-to-one and hence one cannot recover the continuous-time system from its discretized model without further information. Here, we show that it is possible to reconstruct a continuous-time rational transfer function based on discretized models at several, suitably chosen, sampling rates. The dual results in discrete time are also studied: reconstruction of discrete-time systems is possible based on several down-sampled versions.