Partial realization of 2-D discrete linear system and 2-D Pade approximation and reduction of 2-D rational transfer function

Abstract

A method is presented for determining the unknown degree and system function of any 2-D discrete linear shift-invariant system characterized by a 2-D impulse response array, i.e., the coefficients of the formal double power series that are obtained by expanding a rational transfer function. Problems of 2-D Pade approximation and 2-D system reduction can be solved by the same method by making a reasonable assumption in the context of 2-D linear systems theory. The method is based on a 2-D extension of the Berlekamp-Massey algorithm for synthesis of linear feedback shift registers. It gives a novel approach to identification and approximation of 2-D linear systems and is comparable in efficiency with other methods for 2-D rational approximation based on the block Toeplitz and block Hankel matrices.