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An iteratively weighted minimax method is proposed for designing finite-impulse-response (FIR) variable fractional-delay (VFD) digital filters whose peak errors of variable frequency response (VFR) and VFD response are simultaneously suppressed. The basic idea of this new minimax design tries to minimize a mixed error function that contains both the VFR peak error and VFD peak error, and the two peak errors are weighted by a weighting factor λ. By linearizing the highly non-linear constraints on the VFD errors, we can solve this co-minimization problem using the well-known software SeDuMi. As a result, both the VFR peak error can be significantly reduced as compared with the existing minimax design that minimizes only the VFR peak error. A design example is given to verify its effectiveness.