Minimal circuit and state space realization of three-term separable denominator 2-D filters

A simple method is presented for the minimal state space realization of two dimensional (2-D) filters, with a three-term separable denominator (3TSD) made up of two 1-D and one 2-D terms. The matrix A and the vectors b and c of the state space model are derived explicitly from the coefficients of the initial transfer function. The circuit implementation for the 2-D 3TSD filters is provided, as well. The number of delay elements employed represents a significant reduction compared to earlier non-minimal realizations.