Optimal synthesis of 2-D separable-denominator filter structures based on 1-D frequency-weighted sensitivity minimization

An efficient technique is developed for synthesizing two-dimensional (2-D) separable-denominator filter structures with low sensitivity. A 2-D separable-denominator filter is decoupled into two 1-D filters. The sensitivity of a 2-D separable-denominator filter is analyzed in term of each 1-D filter and is evaluated independently by using two performance measures. By minimizing two performance measures individually, 2-D separable-denominator filter structures with low sensitivity are synthesized in unconstraint case and in the case of scaling constraints on the state variables. It is also clarified that the balanced realization is not a minimum sensitivity realization for a 2-D separable-denominator filter. Finally, a numerical example is given to illustrate the utility of the proposed technique.