On the weighted sensitivity minimization of 2-D state-space digital filters

This paper considers the problem of synthesizing the optimal finite word length two-dimensional state-space filter structures that minimize weighted sensitivity. First, a frequency-weighted sensitivity measure is defined in place of the usual sensitivity measure. A novel technique is then developed for finding the set of the optimal filter structures that minimize this frequency-weighted sensitivity measure over all the similarity transformations. The optimal solution is analytically obtained in a closed form. Finally, a numerical example is given to illustrate the utility of the proposed technique.