The so-called zero-order hold (ZOH) discretization or step-invariant transf
ormation is not one-to-one and hence one cannot recover the continuous-time
system from its discretized model without further information. Here we sho
w that it is possible to reconstruct a continuous-time rational transfer fu
nction based on discretized models at several, suitably chosen, sampling ra
tes. The dual results in discrete time are also studied: Reconstruction of
discrete-time systems is possible based on several down-sampled versions.