Simultaneous minimization of pole and zero sensitivity in digital filter design

The simultaneous pole and zero sensitivity minimization problem is investigated with respect to the realizations of a digital filter. The necessary and sufficient condition is given for the optimal realizations, which minimize the zero sensitivity subject to a minimal pole sensitivity. These realizations are those that minimize simultaneously pole and zero sensitivity if the latter exists. An iterative algorithm is proposed to find the optimal realizations. A numerical example is given which confirms the theoretical results