Coefficient Symmetry for Implementing Odd-Order Lagrange-Type Variable Fractional-Delay Filters

Lagrange-type variable fractional-delay (VFD) filters are simple and fundamental tools for high-resolution image interpolation. In this paper, we first reveal and theoretically prove the coefficient-symmetry of odd-order Lagrange-type VFD filters, and then exploit the coefficient-symmetry in implementing the VFD filters. We show that the odd-order Lagrange-type VFD filters can be efficiently implemented as the Farrow structure and even-odd structure, whose subfilters have mostly symmetric or antisymmetric coefficients. Thus, the storage cost for the subfilter coefficients can be reduced by 50%, and the number of multiplications required for VFD filtering can also be reduced by 50%, which facilitates high-speed signal processing