An effective technique for the synthesis of an equiripple low pass prototype filter with asymmetric frequency response and arbitrary transfer function zeros

A simple numerical technique (based on polynomial fitting) is presented which allows to determine the poles of a general low-pass, frequency asymmetric, prototype filter (both of even or odd order) with equiripple Cebycheff passband response. The zeros of the transfer function can be arbitrarily specified in the complex plane (however they must be symmetric with respect to the imaginary axis). Once the poles are known, the synthesis of the filter is carried out through the chain matrix polynomials, obtaining a general cross-coupled structure. As an example of application, the synthesis of a group delay equalized filters with a prescribed transmission zero in the lower stop band is presented.