LINEAR MULTIVARIATE MODELS FOR PHYSIOLOGICAL SIGNAL ANALYSIS - THEORY

The general linear parametric multivariate modelling concept is presen ted. This model combines a variety of different kinds of multivariate linear models. The concept of partial spectral analysis is derived fro m the general model. Some emphasis is laid on the causality demands of the model, and it is shown that the classic strictly-causal structure must be abandoned in order to utilise the modelling in many practical situations. Two special sub-class models are described in detail: the multivariate autoregressive model and the multivariate dynamic adjust ment model. Furthermore, time-varying modelling is considered. The mod elling of the real system is presented on a general level as a system identification cycle. The application of the methods to real physiolog ical data is,presented in the companion paper.