Design of fractional delay filter using discrete Fourier transform interpolation method

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. Next, design examples are demonstrated to show that the proposed DFT method has a smaller design error than those of the conventional Lagrange and window fractional delay FIR filters when using the same design parameters. Finally, the designed DFT-based fractional delay FIR filter is applied to design a digital differentiator and half-band filter.