A generalized technique for the synthesis of 2-D state-space digital filters with minimum roundoff noise

A generalized technique has been developed for the synthesis of 2-D state-space filter structures which minimize the roundoff noise under a scaling constraint. This is based on the Fornasini-Marchesini local-state-space (LSS) model. The optimal filter structure is found using a 2-D similarity transformation characterized by a nonsingular matrix which is not block-diagonal, but general. This allows one to synthesize the optimal filter structure by solving only one optimization problem. If some constraints are imposed on the Fornasini-Marchesini LSS model and the 2-D similarity transformation matrix, it is possible to easily arrive at the results based on the Roesser LSS model. The proposed theory is therefore quite general and simple.<>