A General Tchebycheff Rational Function

The principal result of this paper is the derivation of a general rational function having arbitrary poles which approximates zero with a Tchebycheff characteristic. It is shown how this function can be used to obtain transfer functions which possess a Tchebycheff, low-pass filter characteristic and for which either the poles or zeros are arbitrary. Two applications for this function are given: (1) low-pass RC filters having a specified ripple in the pass band, and (2) low-pass filters having a specified ripple in the pass band and points of infinite attenuation at arbitrary frequencies outside the pass band.