The evaluation of cross-correlation sequences for 2D ARMA processes [recursive filters

Abstract

This paper presents a general method of evaluating cross-correlation sequences and double-complex integrals for two-dimensional autoregressive moving average processes. The method is based on treating the rational-form integrand in a double-complex integral as a function of one complex variable, while its coefficients are functions in another complex variable. It involves solving a symbolic Diophantine equation with the Euclid algorithm and finding roots or performing spectral factorization, with respect to the unit circle for four one dimensional polynomials. To illustrate the proposed method, three examples are provided.