Roundoff noise minimization in state-space digital filtering

For the class of digital filters described by the state equations, a new expression for the roundoff noise and the dynamic range constraint equations have been established. Then, minimization of the roundoff noise subject to the l2norm dynamic range constraint is considered. In particular, a lower bound and the global minimum of the unit noise, i.e., the noise generated under the assumption that each state equation contains exactly one noise source, have been obtained. A method of realizing the minimum unit noise filter, along with a numerical example is also given.