To satisfy the requirement on high-precision differentiation of narrow-band signals and low delay of the differentiator

this paper presents a design method for low-delay finite impulse response flat digital differentiators. The method minimizes the maximum magnitude error subject to flatness and phase-error constraints on the differentiator. By eliminating the flatness constraint with the general solution of linear equations

we ensure that the differentiator has desired flatness degrees. By reweighting the phase error with group-delay error

the method reduces the passband group-delay error of the differentiator. Design examples and comparisons with literature methods show the effectiveness and superiority of the proposed method.