Extended Remez algorithms for filter amplitude and group delay approximation

Various Remez-type algorithms for the computation of rational filter functions of a general form are proposed. They allow filter amplitude and group delay functions to be arbitrarily shaped and tapered. Such functions can be applied to predistort for undesirable effects in communication systems such as sinc (x), transmission line weighting or distortion due to nonideal components. High-order touch points are introduced as a generalisation of the concept of maximum flatness. They are used to trade off between the amplitude, group delay and passive sensitivity properties of a filter. The high-order touch points can be used directly to design a passive ladder prototype by an iterative algorithm.