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In this paper, the design of fractional delay FIR filter is investigated. First, the interpolation formula of a discrete-time sequence is derived by using discrete Fourier transform (DFT). Then, the DFT-based interpolation formula is applied to design fractional delay FIR filter by using suitable index mapping. The filter coefficients are easily computed because a closed-form design is obtained. Finally, design examples are demonstrated to show that the proposed DFT method has smaller design error than those of the conventional window and Lagrange fractional delay FIR filters when using the same design parameters.