On l2-Sensitivity for Generalized Direct-Form II Structure of 2-D Separable-Denominator Filters

A new expression of evaluating l2-sensitivity for generalized direct-form II structure of two-dimensional (2-D) separable-denominator digital filters is derived and analyzed. Unlike the previous work, l2-sensitivity is analyzed for the filter structure instead of its state-space realization. Then the resulting l2-sensitivity measure is compared with that deduced in a recent study of generalized direct-form II state-space realization of 2-D separable in denominator digital filters. In a numerical example, the new l2-sensitivity measure is minimized with respect to free parameters subject to l2-scaling constraints by an exhaustive search over a set of discrete values of finite cardinality, and the results are compared with those obtained by existing techniques.