Design of Minimum Noise Digital Filters Using a Mixed Norm.
RHODE ISLAND UNIV KINGSTON DEPT OF MATHEMATICS
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A concept of a mixed norm of a function is introduced and studied. It arises from the problem of design of nonrecursive digital filters. Previous work on design of nonrecursive digital filters which are identical mathematically to uniformly-spaced linear antenna arrays, has minimized a quadratic error criterion, subject to inequality constraints on the maximum error in the filter approximation, at an arbitrary but finite number of points. Quadratic error and maximum error can be made to correspond, respectively, to total stopband noise power and maximum passband error at a single frequency. A weighted sum of the two error criteria will be minimized by use of quadratic programming. Furthermore, any solution to the constrained quadratic minimization problem will be shown to be a solution to a weighted sum minimization problem, and vice versa.
- Theoretical Mathematics