Estimation of the Magnitude Squared Coherence Spectrum Based on Reduced-Rank Canonical Coordinates

In this paper, a new technique for the estimation of the magnitude squared coherence (MSC) spectrum is proposed. The method is based on the relationship between the MSC and the canonical correlation analysis (CCA) of stationary time series. Particularly, the canonical correlations coincide asymptotically with the squared roots of the MSC, which is exploited in the paper to obtain an estimate of the MSC based on a reduced-rank version of the estimated coherence matrix. The proposed technique provides a higher spectral resolution than the well-known Welch's method, and it also avoids the signal mismatch problem associated to the minimum variance distortionless response (MVDR) based approach. Finally, the performance of the proposed method is evaluated by means of some numerical examples.