On the use of remes multiple exchange algorithm for linear-phase FIR filters with general specifications

The celebrated Remes multiple exchange algorithm for linear-phase digital F IR filter design is most commonly described for ordinary filter types (low- pass, high-pass, etc.) where it is sufficient to consider only the magnitud e of the error function, Convergence for general specifications will be gua ranteed only when the sign of the error function is incorporated. However, a discussion of this feature of the Remes algorithm is lacking in the liter ature on digital signal processing. The aim of this presentation is to fill in this gap by recasting the Remes exchange algorithm for the design of li near-phase finite-impulse response (FIR) filters with a general amplitude r esponse specification.