A STATE-SPACE APPROACH TO DISCRETE-TIME SPECTRAL FACTORIZATION

The classical state-space approach to continuous-time spectral factorization is used to develop a method for discrete-time spectral factorization. This results in a quadratic matrix equation, which is referred to here as the modified algebraic Riccati equation (MARE). Solving this equation for the factorizing solution constitutes the major part of the computation needed to obtain the spectral factor. Recently developed approaches to the analysis and solution of the matrix Riccati equation encountered in continuous-time control and filtering problems are adapted for use here.