High-Speed and Low-Cost Structures for Implementing Odd-Order Lagrange-Type Variable Fractional-Delay Filters

We have derived an explicit formula for computing the coefficients of arbitrary-order Lagrange-type variable fractional-delay (VFD) digital filter in a closed-form. This paper develops a coefficient symmetry for efficiently implementing odd-order Lagrange-type VFD filters such that an odd-order Lagrange-type VFD filter can be implemented as the Farrow structure and more efficient even-odd structure whose all sub-filters have either symmetric or anti-symmetric coefficients. This symmetry exploitation not only saves the storage for VFD filter coefficients and but also reduces the number of multiplications required in VFD filtering by 50%, which speeds up the VFD filtering process.