Design of fractional delay FIR filter using discrete cosine transform

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