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

Abstract

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 low-pass 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.