A robust initialization scheme for the Remez exchange algorithm

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/sub /spl infin// 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 design problems.