Robust Structure Transformation for Causal Lagrange-Type Variable Fractional-Delay Filters

We have rigorously proved that an odd-order causal Lagrange-type variable fractional-delay (VFD) digital filter can be implemented as the Farrow structure with symmetric or antisymmetric subfilters through utilizing matrix transformation. This paper reveals a numerical problem that occurs in the matrix transformation due to the so-called catastrophic cancellation in numerical computation. Our computer simulations have verified that utilizing the matrix transformation can get numerically stable solutions for the VFD filter whose order N is below about 20, but fails for higher order cases. To solve this problem, we present a robust approach to the structure transformation for both even- and odd-order causal Lagrange-type VFD filters, which does not rely on matrix operations and, thus, can yield numerically stable solutions even for high-order cases. Moreover, the symmetry and antisymmetry of the subfilter coefficients after the robust structure transformation are also rigorously proved. Numerical examples are included to illustrate the robustness of the proposed structure transformation and show the coefficient symmetries.