L2-sensitivity analysis and minimization of 2-D separable-denominator state-space digital filters

For two-dimensional (2-D) state-space digital filters that are separable in the denominator, the coefficient sensitivity is analyzed by using a pure L₂-norm, and then, the problem of minimizing the L₂-sensitivity is considered. First, a novel expression is developed in closed form for the evaluation of the L₂-sensitivity. Next, an iterative procedure is presented for synthesizing the optimal filter structures that minimize the L₂-sensitivity. Finally, a numerical example is given to illustrate the utility of the proposed technique.