Fractional delay filter design based on truncated lagrange interpolation

A new design method for fractional delay filters based on truncating the impulse response of the Lagrange interpolation filter is presented. The truncated Lagrange fractional delay filter introduces a wider approximation bandwidth than the Lagrange filter. However, because of truncation, a ripple caused by the Gibbs phenomenon appears in the filter's frequency response. Proper choices of filter order and prototype filter order allow adjusting the overshoot to a desired level and simultaneously reducing the overall frequency-response error. The design of the proposed filter is computationally efficient, because it is based on polynomial formulas, which have common terms for all coefficients.