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

This paper is concerned with the reduction of roundoff noise effects subject to l₂-scaling constraints for state-space digital filters by means of high-order error feedback and realization. First, the roundoff noise gain is mimimized subject to l₂-scaling constraints by choosing the coordinate transformation matrix appropriately. Optimal high-order error-feedback matrices are then determined so as to minimize the roundoff noise gain in the state-space digital filter transformed by the resulting coordinate transformation matrix. Finally a numerical example is presented to illustrate the utility of the proposed technique.