Variance and covariance computations for 2-D ARMA processes

An algorithm is presented to compute the variance of the output of a two-dimensional stable autoregressive moving-average (ARMA) process driven by a white noise bi-sequence with unity variance. The algorithm is dedicated to the evaluation of a complex integral and is based on partial-fraction decomposition. The partial-fraction decomposition involves only efficient discrete Fourier transform computations for the inversion of a matrix polynomial, and the value of the complex integral is determined by the residue method with finding the roots of a one-dimensional polynomial. The algorithm is easy to implement and it can be extended to the covariance computation for two 2-D ARMA processes.