Typical Benchmark Specifications for Designing Stable Variable Filters Using Novel Unity-Bounded Functions

Abstract

This paper first presents six (6) types of benchmark amplitude design specifications, including variable low-pass specification, variable high-pass specification, variable bandpass specification, variable bandstop specification, variable notch-frequency specification, and variable notch-width specification. The design specifications can be taken as typical benchmark specifications targeted at testing as well as validating the effectiveness of various newly developed algorithms for designing various typical variable filters (VFs). Then, the paper provides a novel unity-bounded (UB) function developed for ensuring the stability of those VFs with recursive structures. Finally, a wide variety of simulation results are included for validating the design performance as well as the assured stability by using both the benchmark design specifications and the novel UB function.