Reconstruction of continuous-time systems from their discretizations

The so-called ZOH discretization or step-invariant transformation is not one-to-one and hence one can not 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 results also relate to the problem of reconstructing continuous-time signals with rational Laplace transforms from their sampled versions at diierent rates.