Three-band filter: user's manual

Optimal synthesis of multi-band electrical filters is based on the rational approximation problem, which is a multi-zone extension of the classical third or fourth Zolotarev problem. It is believed that the three-zone problem was solved by Edward Stiefel in 1960. In the talk we will offer a geometric interpretation of Stiefel's formulas, from which it follows that Stiefel's solution is incomplete, i.e. it does not serve all configurations of the three working filter bands. Missing designs of solution will be proposed and their completeness will be shown.