Recent Progress in Optimization of Multiband Electrical Filters

TL;DR

This paper reviews recent advances in optimizing multiband electrical filters, leveraging algebraic geometry techniques to improve filter synthesis based on classical mathematical approximations.

Contribution

It introduces a novel algebraic geometry-based approach for solving optimization problems in multiband filter design, extending Zolotar"ev's rational approximation methods.

Findings

Enhanced filter optimization techniques using algebraic geometry.

Generalization of Zolotar"ev's rational approximation for multiband filters.

Potential improvements in filter performance and synthesis efficiency.

Abstract

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.