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The celebrated Remes multiple exchange algorithm for linear-phase digital FIR filter design is most commonly described for ordinary filter types (low-pass, high-pass, etc.) where it is sufficient to consider only the magnitude of the error function. Convergence for general specifications will be guaranteed only when the sign of the error function is incorporated. However, a discussion of this feature of the Remes algorithm is lacking in the literature 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 linear-phase finite-impulse response (FIR) filters with a general amplitude response specification.