Coefficient Symmetry and Efficient Implementation of Lagrange-Type Variable Fractional-Delay Filters

We have theoretically proved the Liu-Wei´s closed-form formula for computing the coefficients of one-dimensional (1-D) variable fractional-delay (VFD) finite-impulse-response (FIR) digital filter derived from nonlinear interpolating polynomial. In this paper, we reveal the symmetry of the VFD filter coefficients and exploit the coefficient symmetry in evaluating the VFD filter frequency characteristics with reduced computational complexity. The coefficient symmetry is also exploited in efficiently implementing the VFD filter as Farrow structure and even-odd structure for high-speed signal processing