Polynomial Filters with Controllable Overshoot In Their Step Transient Responses

Abstract

The paper considers a new class of polynomial filters which is an extension of the Bessel (Thomson) filters. This extension is achieved considering the difference of two weighted Bessel polynomials. The weight of the subtracted polynomial is including the multiplier an the choice of which defines the class of resulting filters. When an = 0 one obtains the transfer functions of regular Bessel (Thomson) filters. When an =1 one obtains the Stokes filters. The Stokes filters are faster than Bessel filters but have larger step response overshoot. Using the range of −1 < an ≤ 2 one obtains the stable filters with controllable step transient response overshoots. The upper border for an is defined by the stability condition of higher order filters, the low border is defined by the non-monotonicity conditions.