A Subspace Algorithm for the Identification of Discrete Time Frequency Domain Power Spectra

In this paper we present a new subspace algorithm for the identification of multi-input multioutput linear discrete time systems from measured power spectrum data. We show how the state space system matrices can be determined by taking the inverse Fourier transform of the given data and applying the result to a new realization algorithm. Special attention is paid to the positivity of the identified power spectrum. The computational speed is improved by applying a Lanczos algorithm. The algorithm is illustrated with two practical examples. 1 Introduction Identification of multi-input multi-output (MIMO) systems from a measured power spectrum is still considered to be a challenge. This type of data typically arises when modeling disturbances, in which case the frequency domain power spectrum is often easily obtained. The algorithm described in this paper determines a state space realization of this power spectrum. For disturbance modeling, the spectral factor of this power spectrum ca..