A parametric method for computing magnitude squared coherence

The magnitude squared coherence (MSC) is widely used as a measure of the similarity between a pair of signals. It is normally defined as the squared magnitude of the two signals´ cross-spectrum divided by the product of their autospectra. Many methods exist for computing the MSC. The required spectra are normally computed via averaged periodograms. Recently some new algorithms based on the parametric estimation of transfer functions have been developed [1,2,3]. This paper presents such a method based on autoregressive moving average (ARMA) difference equations. The method uses the singular value decomposition (SVD) to determine the ARMA model orders as well as the ARMA parameter estimates. A class of problems, which can be solved by our method, is described. The performance of the algorithm is verified via a simulation study of a problem proposed in [1].