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A new method for designing linear-phase finite impulse response (FIR) filters is proposed by using the blockwise waveform moments. The proposed method yields linear-phase FIR filters whose magnitude response and its derivatives to a certain order take the prescribed values at equally spaced frequency points. The design procedure only needs to solve a system of linear equations, whose size is slightly smaller than the degree of the resulting filter. In addition, the inversion of the linear equations can be essentially precomputed. Therefore, the proposed design method is computationally efficient. In particular, for some important cases, i.e., the maximally flat R-regular Lth-band FIR filters, a closed-form formula can be obtained. It is also shown that the resulting R-regular Lth-band FIR filters have the zero intersymbol interference property.