Some improvements to the design programs for equiripple FIR filters

Some methods are proposed which try to improve the execution of FIR filter design programs based on the Remez algorithm. The number of evaluations of the Lagrange interpolation formula needed for finding the extrema of the error function can be reduced by searching for the zeros of the derivative. The derivative of the Lagrange interpolation polynomial can be computed together with the Lagrange interpolation itself with little additional effort. The precision of the evaluation of the Lagrange interpolation can be improved by utilizing all the points resulting from the Remez algorithm. A couple of other minor improvements are given, too.