Optimal FWL design of state-space digital systems with weighted sensitivity minimization and sparseness consideration

The optimal finite word length (FWL) state-space digital system problem is investigated. Instead of the unusual sensitivity measure, it is argued that it may be desirable to minimize a frequency weighted sensitivity measure over all similarity transformations. The set of optimal realizations minimizing this weighted sensitivity is completely characterized, and an algorithm is proposed to find the optimal solution set. It is shown that a subset of the optimal realization set consists of sparse Schur realizations, whose actual sensitivity (taking into account the zero elements) is even smaller than the theoretical minimal sensitivity. Some properties of the Schur realizations are discussed. A numerical example that confirms the theoretical results is given