Recent Progress in Optimization of Multiband Electrical Filters

Abstract

The best uniform rational approximation of the \emph{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 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.