Spectral decomposition in multichannel recordings based on multivariate parametric identification

A method of spectral decomposition in multichannel recordings is proposed, which represents the results of multivariate (MV) parametric identification in terms of classification and quantification of different oscillating mechanisms. For this purpose, a class of MV dynamic adjustment (MDA) models in which a MV autoregressive (MAR) network of causal interactions is fed by uncorrelated autoregressive (AR) processes is defined. Poles relevant to the MAR network closed-loop interactions (cl-poles) and poles relevant to each AR input are disentangled and accordingly classified. The autospectrum of each channel can be divided into partial spectra each relevant to an input. Each partial spectrum is affected by the cl-poles and by the poles of the corresponding input; consequently, it is decomposed into the relevant components by means of the residual method. Therefore, different oscillating mechanisms, even at similar frequencies, are classified by different poles and quantified by the corresponding components. The structure of MDA models is quite flexible and can be adapted to various sets of available signals and a priori hypotheses about the existing interactions; a graphical layout is proposed that emphasizes the oscillation sources and the corresponding closed-loop interactions. Application examples relevant to cardiovascular variability are briefly illustrated.