Transformation matrix for odd-order Lagrange-type variable fractional-delay filters

Lagrange-type variable fractional-delay (VFD) digital alters can be directly implemented as the well-known Farrow structure, but the fixed-coefficient filters (subfilters) do not have symmetric or anti-symmetric coefficients. This paper presents a transformation matrix for transforming a causal odd-order Lagrange-type VFD filter into a new one whose all the subfilters have either symmetric or anti-symmetric coefficients. As a result, the number of multipliers can be reduced by almost 50%, which not only speeds up the VFD filtering process, but also saves the cost for storing the independent subfilter coefficients.