Minimization of pole/zero sensitivity in digital filter design with sparse structure consideration

In this paper, we consider the problem of optimal pole/zero sensitivity realization with sparse structure consideration. Noting the fact that optimal realizations are fully parametrized and that the optimal realizations are not unique, the optimal sparse realizations are found based on Hessenburg and Schur forms. An algorithm is developed for finding further sparse realizations, which can yield a satisfying performance and has much less parameters to implement than a general optimal realization. A numerical example is presented to show the design procedure and the performance of the algorithm