Spectral estimation in frequency-domain by subspace techniques

In this paper, frequency-domain subspace-based algorithms are proposed to estimate discrete-time cross-power spectral density (cross-PSD) and auto-power spectral density (auto-PSD) matrices from samples of the Welch cross-PSD and auto-PSD estimators on uniform grids of frequencies. The proposed algorithms are shown to be strongly consistent. A link between the well-known time-domain covariance-based estimation methods and the frequency-domain realization-based methods of this paper is also established. The consistency of the proposed algorithms is not expected a priori since the periodograms are not consistent spectrum estimators even if the true power spectrum is rational. The algorithms are tested on numerical examples and a real-life application example concerned with the modeling of acoustic spectra for fault detection in induction motors.