Projective view at optimization problem for multiband filter
Copyright policy )Projective view at optimization problem for multiband filter
The best uniform rational approximation of the \emph{sign} function on two intervals separated by zero was explicitly solved by E.I. Zolotarëv in 1877. This optimization problem is the initial step in the staircase of the so called approximation problems for multiband filters which are of great importance for electrical engineering. We show that known in the literature optimality criterion for this problem may be contradictory since it does not take into account the projective invariance of the problem. We propose a new consistently projective formulation of this problem and give a constructive optimality criterion for it.
15 pages, 4 figures, minor corrections compared to V1
- Russian Academy of Sciences Russian Federation
- Institute of Numerical Mathematics Russian Federation
- Department of Mathematical Sciences Russian Federation
equiripple property, Circuits in qualitative investigation and simulation of models, Stiefel class, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, alternation, Best approximation, Chebyshev systems, Approximation by rational functions, Optimality conditions for minimax problems, optimization of electrical filters, FOS: Electrical engineering, electronic engineering, information engineering, uniform rational approximation, ansatz method
equiripple property, Circuits in qualitative investigation and simulation of models, Stiefel class, Systems and Control (eess.SY), Electrical Engineering and Systems Science - Systems and Control, alternation, Best approximation, Chebyshev systems, Approximation by rational functions, Optimality conditions for minimax problems, optimization of electrical filters, FOS: Electrical engineering, electronic engineering, information engineering, uniform rational approximation, ansatz method
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