Jointly Optimized Error-Feedback and Realization for Roundoff Noise Minimization in a Class of 2-D State-Space Digital Filters

The separate/joint optimization techniques of error-feedback and realization are explored so as to reduce or minimize the effects of roundoff noise subject to l₂-scaling constraints for a class of 2D state-space digital filters. First, the joint optimization problem at hand is converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the resultant unconstrained problem is solved iteratively by applying an efficient quasi-Newton algorithm. Finally, a numerical example is presented to illustrate the utility of the proposed techniques.