Rational approximation of 2-D linear discrete systems

In this paper we present an efficient procedure to obtain a rational model for a 2-D linear shift-invariant, discrete system using first- and second-order data from it. This procedure is a modification of the nonlinear least-squares approximation, and it generalizes the Padé approximants and the spectral estimation modeling procedures. The parameters of the approximating filter are obtained by solving a system of linear equations by means of an efficient recursive algorithm which is developed using the relation of the approximation problem with the theory of orthogonal polynomials on the unit bidisk. We discuss some of the algebraic properties of the solution and apply them to define cases for which the BIBO stability of the approximating filters is ensured. The proposed procedure finds applications in the design and stabilization of 2-D recursive digital filters and in the autoregressive moving average (ARMA) modeling of stationary random fields.