L2-Sensitivity Analysis and Minimization for Generalized Direct-Form II Realization of 2-D Separable-Denominator Digital Filters

In this paper, l 2 -sensitivity for the generalized direct-form II state-space realization of two-dimensional (2-D) separable-denominator digital filters is analyzed and minimized with respect to free parameters subject to l 2 -scaling constraints. Improved l 2 -sensitivity for 2-D separable-denominator digital filters is investigated by taking 0 and ±1 elements into account. An l 2 -sensitivity measure for the generalized direct-form II state-space realization of 2-D separable-denominator digital filters is deduced by applying improved l 2 -sensitivity. The l 2 -sensitivity measure is then minimized with respect to free parameters subject to l 2 -scaling constraints by employing an exhaustive search over a set of discrete values of finite cardinality. A numerical example is included to illustrate the validity and effectiveness of the proposed technique.