Generalization of Bessel (Thomson), Stokes and Quasi-Butterworth Filters

The paper considers a new class of polynomial filters which includes Bessel (Thomson), Stokes and Quasi-Butterworth (filters of the same overshoots, but with faster rise time than the Butterworth ones) filters as particular cases. The transfer functions of all these filters are derived using the difference of two weighted Bessel polynomials. The parameter included in the weight of the subtracted polynomial defines the class of the resulting transfer function. The choice of this parameter to obtain Bessel (Thomson) or Stokes filters is direct, but the value of this parameter to obtain the Quasi-Butterworth filters requires calculation of the step-transient response overshoot. The example of comparison included in the paper describes the full set of forth order filters. In addition, the paper presents the transfer functions of the Quasi-Butterworth filters from the second to the eight order.