Parameterized Even-Symmetric Function for Stabilizing and Designing Variable Lowpass Filters
Tian–Bo Deng · 2024
A variable filter (VF) is capable of tuning its frequency-domain response promptly without redesigning a novel filter. Despite the fact that a recursive VF requires less computations as compared with its non-recursive counterpart, it faces a challenging stability issue. The stability issue can be skillfully resolved through replacing the coefficients in the VF's denominator by using some special functions of other parameters. Replacing the denominator coefficients with such special functions enables the stability requirement to be always satisfied without any con-cerns about the values of the new parameters. To perform those parameter replacements, a function (unity-bounded function: UB function) must be used. The UB function needs to meet a special condition. In this paper, such a UB function is presented for carrying out the denominator-parameter replacements, which is an even-symmetric function. Furthermore, this even-symmetric UB function is employed in designing a recursive variable-lowpass-filter, and computer simulations are given for showing the assured stability and achieved high accuracy.