Transfer function estimation as an inverse problem

We take the view that the transfer function (TF) of a linear system is an infinite dimensional parameter and observe that estimation of it from input-output data is an ill-conditioned inverse problem. We exhibit minimax lower bounds that limit the precision that any estimator can attain, noting that these depend on prior knowledge of the TF. We review various regularization leased methods of TF estimation. Some connexions with information based complexity are sketched