Stokes polynomial filters

Abstract

The paper considers a new class of filters with transfer functions using the polynomials introduced by the British physicist Sir G.G. Stokes. The filters are transitional between Bessel and Butterworth ones. When one compares the step-responses of Bessel, Stokes, and Butterworth filters of the same order and the same -3dB bandwidth then the result is following. The Bessel filters have a certain delay and (practically) no overshoot in their step-transient response. The Stokes filters have larger delay than Bessel filters and a small overshoot. Finally, the Butterworth filters have largest delay and largest overshoot. The paper illustrates these properties and describes the data required for synthesis of the Stokes filters.