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Approximation and Optimization pp 135–149Cite as

Recent Progress in Optimization of Multiband Electrical Filters

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 145))

Abstract

The best uniform rational approximation of the sign function on two intervals was explicitly found by Russian mathematician E.I. Zolotarëv in 1877. The progress in math eventually led to the progress in technology: half a century later German electrical engineer and physicist W. Cauer on the basis of this solution has invented low- and high-pass electrical filters known today as elliptic or Cauer-Zolotarëv filters and possessing the unbeatable quality. We discuss a recently developed approach for the solution of optimization problem naturally arising in the synthesis of multi-band (analogue, digital or microwave) electrical filters. The approach is based on techniques from algebraic geometry and generalizes the effective representation of Zolotarëv fraction.

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Acknowledgements

Supported by RScF grant 16-11-10349.

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Authors and Affiliations

  1. Institute for Numerical Mathematics, Russian Academy of Sciences, Moscow, Russia

    Andrei Bogatyrëv

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  1. Andrei Bogatyrëv
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Editors and Affiliations

  1. Department of Economics, University of Athens, Athens, Greece

    Ioannis C. Demetriou

  2. Department of Industrial & Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos

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Bogatyrëv, A. (2019). Recent Progress in Optimization of Multiband Electrical Filters. In: Demetriou, I., Pardalos, P. (eds) Approximation and Optimization . Springer Optimization and Its Applications, vol 145. Springer, Cham. https://doi.org/10.1007/978-3-030-12767-1_8

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