A robust initialization scheme for the Remez exchange algorithm

Abstract

A well-known least squares optimum approximation method is proposed as an efficient initialization scheme for the Remez exchange algorithm. More specifically, we theoretically demonstrate that the "don't care" least squares optimum solution guarantees, inside the bands of interest, the correct number of alternating in-sign extrema of the error function, thus satisfying one of the two basic conditions that are sufficient for obtaining the L. optimum solution. Although convergence of Remez is theoretically assured, its practical implementations may fail to converge in "difficult" design problems when classical initialization is used. In particular, Matlab's realization of Remez,,when initialized with the proposed scheme, exhibits a significantly better overall performance that translates into faster convergence and more robust behavior, especially in difficult designs problems.