Property of Rational Functions Related to Band-Pass Transformation With Application to Symmetric Filters Design

This paper considers the condition when a rational function F(s) may be represented as the function of the argument s + (1/s). If this condition is satisfied then F(s) is the ratio of recursive (symmetric) polynomials. This paper investigates the network properties of such rational functions and their realization. Then the symmetric polynomials are applied for synthesis of symmetric band-pass filters. Substituting p = s + (1/s) into symmetric band-pass filter transfer function one obtains its lowpass generating filter. The slew rate and overshoot of generating filter step-response is closely connected with the step-response duration of symmetric band-pass filter. The choice of generating filter becomes an additional factor of symmetric band-pass filter design. As the generating filters the paper proposes using Lommel polynomial filters which have easy control of overshoot and slew rate. An example of six order symmetric band-pass filter is given.