An optimal order structure for 2-D digital filters

The model approximation as well as implementation of 2D recursive separable-in-denominator (RSD) digital filters with fixed-point arithmetic are investigated. A minimum-order structure is proposed based on the optimality condition of an error criteria due to both approximation and implementation. In order to reduce the number of multiplications for an optimal order realization, a class of second-order structures is proposed. This class of realizations presents a good compromise between low round-off noise, order reduction, number of multipliers and hardware complexity.