Spectral Factorization of Wide Sense Stationary Processes on Z Squared

摘要

A theorem on canonical spectral factorization is proved starting from the canonical representation of a nondeterministic process, set in a framework analoguous to one-parameter prediction theory, in order to study prediction of wide-sense stationary processes on the plane. The theorem is based on one-parameter spectral factorization techniques borrowed from the theory of analytic functions on the unit disk of C, the complex numbers. A class of processes having a quarter-plane canonical representation in terms of its innovations can be studied via the theory of analytic functions on the unit bidisk of the complex plane C square. The case when the causal representation is not causally invertible is considered as is Wold decomposition and filtering.