Minimum uncorrelated unit noise in state-space digital filtering
- 1 August 1977
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Acoustics, Speech, and Signal Processing
- Vol. 25 (4) , 273-281
- https://doi.org/10.1109/tassp.1977.1162971
Abstract
For the class of digital filters described by the state equations, new expressions for the roundoff noise and the dynamic-range constraint equation have been established. Then, minimization of the roundoff noise subject to the l2norm dynamic-range constraint is considered. Using the polar decomposition of a nonsingular matrix, the effects of an equivalent transformation on the noise are analyzed, then, 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, is obtained. A method of realizing the minimum unit noise filter is given, and possible further optimization of the filter is discussed. A numerical example is given to illustrate the computational procedure.Keywords
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