On the use of parametric and non-parametric noise-models in time- and frequency domain system identification

In this paper we start from the observation that there is an exact equivalence between time- and frequency domain identification for finite length data records under the standard conditions of the prediction error framework. Next we study the identification of a nonparametric plant and noise model, in the time- and frequency domain. Finally we discuss the mixed use of parametric plant models and nonparametric noise models in the identification process, and comment its impact on the user choices. It turns out that the availability of a nonparametric noise model simplifies significantly the identification of a parametric plant model. All these results are valid for random, arbitrary, and periodic excitations.