Equiripple approximation design using first order McClellan transformation

Abstract

This paper describes a technique, using the Remez algorithm, to determine the coefficients of the first-order McClellan transformation so that the cut-off frequency of the prototype one-dimensional filter maps onto a contour in the two-dimensional frequency plane which approximates a specified contour in equiripple sense. The type of contours considered are the passband boundaries of circularly symmetric, elliptically symmetric and α°-fan filters. The initial estimate of the transformation coefficients and the cut-off frequency of the one-dimensional filter is obtained analytically. Some of these parameters are then refined using Remez algorithm. Since the initial estimate of the parameters is good, the Remez algorithm converges very rapidly.