Multidimensional spectral factorization and unilateral autoregressive models

In this paper we present a procedure for the spectral factorization of multidimensional spectral density functions. We develop and use properties of the multidimensional spectrum as a basis for the procedure. The resulting factors, like those of Wiener´s one-dimensional factorization, are stable and realizable (i.e., recursible). We describe a numerical algorithm for performing the factorization and indicate its use in obtaining unilateral representations of multidimensional random fields.