  The best uniform rational approximation of the \emph{sign} function on two
intervals was explicitly found by Russian mathematician E.I. Zolotar\"ev 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-Zolotar\"ev 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 Zolotar\"ev fraction.
