Characterization of Stationary Discrete-Time Gaussian Reciprocal Processes over a Finite Interval

Abstract

This paper examines the class of stationary discrete-time multivariate Gaussian reciprocal processes defined over a finite interval [0,N]. The matrix covariance function of such processes obeys a second-order self-adjoint difference equation whose structure is described by a symplectic matrix pencil. The canonical form of symplectic matrix pencils obtained in [Ferrante and Levy, Linear Algebra Appl., 274 (1998), pp. 259--300] is employed to characterize and classify stationary Gaussian reciprocal processes. It is shown that each class of n-dimensional reciprocal processes with fixed reciprocal dynamics is parametrized by n real parameters.