Roundoff noise reduction in 2-D state-space digital filters using high-order error feedback and realization

A technique for reducing roundoff noise effects subject to l₂-scaling constraints is developed for two-dimensional state-space digital filters by means of high-order error feedback and state-space realization. First, the roundoff noise gain is minimized subject to l₂-scaling constraints by choosing the coordinate transformation matrices appropriately. Optimal high-order error-feedback matrices are then determined so as to minimize the roundoff noise gain in the two-dimensional state-space digital filter obtained via the coordinate transformation matrices. Finally a numerical example is presented to illustrate the utility of the proposed technique.