Jointly optimized error feedback and realization for roundoff noise minimization in two-dimensional state-space digital filters

The minimization of roundoff noise subject to l₂-norm dynamic-range scaling constraints in two-dimensional (2-D) state-space digital filters is considered by using joint error feedback and coordinate transformation optimization. An iterative approach for minimizing the roundoff noise under l₂-norm dynamic-range scaling constraints is developed by jointly optimizing a scalar error-feedback matrix and a coordinate transformation matrix. A numerical example is presented to illustrate the utility of the proposed technique.