On the spectral factorization of nonstationary vector random processes

Conditions which depend on the covariance of a vector random process, sufficient to ensure the process can be generated by a linear, invertible system of finite order driven by white noise are derived, and equations which determine the parameters of the system are found. Some structural properties of lumped covariances are given; these stress the close relation between the structure of linear systems and that of lumped covariances and provide a means of establishing the minimal order of generating systems.