Recent Progress in Optimization of Multiband Electrical Filters

The best uniform rational approximation of the sign function on two intervals was explicitly found by Russian mathematician E.I. Zolotarev in 1877. The progress in math eventually led to the progress in technology: half a century later German electrical engineer and physicistW. Cauer on the basis of this solution has invented low- and high-pass electrical filters known today as elliptic or Cauer-Zolotarev 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 Zolotarev fraction.