Identification of Rational Transfer Functions from Sampled Data

We consider the task of estimating an operator from sampled data. The operator, which is described by a rational transfer function, is applied to continuous-time white noise and the resulting continuous-time process is sampled uniformly. The main question we are addressing is whether the stochastic properties of the time series that originates from the sample values of the process allows one to determine the operator. We focus on the autocorrelation property of the process and identify cases for which the sampling operator is injective. Our approach relies on sampling properties of almost periodic functions, which together with exponentially decaying functions, provide the building blocks of the autocorrelation measure. Our results indicate that it is possible, in principle, to estimate the parameters of the rational transfer function from sampled data, even in the presence of prominent aliasing.