New exchange rules for IIR filter design
This paper introduces a new set of exchange rules for a Remez-like algorithm for the Chebyshev design of IIR digital filters. It is explained that the essential difficulty, in applying the Remez algorithm to rational functions, is that on some iterations, there may be no solution to the interpolation problem for which the denominator is strictly non-zero in the interval of approximation. Then the usual procedure for updating the interpolation points cannot be applied. The new rules for updating the interpolation points address precisely this problem for the two-pole case. It is shown with examples that, when the Remez-like algorithm of Hofstetter et al. (1971) is applied to rational functions, there is a way to update the interpolation points so that the algorithm converges rapidly, even when poles arise in the interval of approximation.