Abstract
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 l 2 norm 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.
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