Minimum sensitivity structure of 2-D digital filters based on the Fornasini-Marchesini model

The authors treat the balanced realization and minimum sensitivity structure of two-dimensional (2-D) recursive digital filters. This structure is based on the Fornasini-Marchesini local state-space model. First, a technique is introduced for the balanced realization of 2-D recursive digital filters. Next, the sensitivities of a 2-D transfer function are investigated with respect to coefficients of the local state-space model. The overall sensitivity is then evaluated using the 2-D controllability and observability Gramians. It is also shown that the minimum sensitivity structure is easily derived from the balanced realization and under an l/sub 2/ scaling constraint it is equivalent to that with minimum roundoff noise.<>