Dual time–frequency domain system identification

In this paper we obtain the maximum likelihood estimate of the parameters of discrete-time linear models by using a dual time–frequency domain approach. We propose a formulation that considers a (reduced-rank) linear transformation of the available data. Such a transformation may correspond to different options: selection of time-domain data, transformation to the frequency domain, or selection of frequency-domain data obtained from time-domain samples. We use the proposed approach to identify multivariate systems represented in state–space form by using the Expectation–Maximisation algorithm. We illustrate the benefits of the approach via numerical examples.