Recent Progress in Optimization of Multiband Electrical Filters
This work provides a novel theoretical framework for filter designers to solve a long-standing optimization problem in multiband filter synthesis.
The paper presents a new algebraic geometry-based approach for optimizing multiband electrical filters, generalizing Zolotarëv's rational approximation method to achieve optimal performance.
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.