A computationally efficient coefficient update technique for Lagrange fractional delay filters

A new algorithm for coefficient update of the Lagrange fractional delay FIR filter is proposed, which reduces the computational complexity dramatically. It is based on rearranging the polynomial terms of the Lagrange interpolation formula and computing the common product terms only once. Reordering the Lagrange interpolation formula yields two other methods for updating the coefficients, the direct and the division- based methods. The division-based method uses only one division per coefficient. The two latter methods reduce the computational load, although they are not as efficient as the new algorithm. Finally, the superiority of the direct form FIR implementation of the Lagrange fractional delay filter and the new coefficient update method over other existing methods is demonstrated in an audio signal processing application.