Efficient implementation of odd-order lagrange-type variable fractional-delay digital filters

Lagrange-type variable fractional-delay (VFD) digital filters can be directly implemented as the well-known Farrow structure, but the subfilter coefficients are not symmetric or anti-symmetric. This paper presents a method for transforming an odd-order Lagrange-type VFD filter into a new one whose more than half subfilters have symmetric or anti-symmetric coefficients, which leads to an efficient implementation that reduces the computational complexity required in the VFD filtering process and saves hardware cost for storing independent subfilter coefficients. Several interesting symmetric properties of the resulting subfilter coefficients are rigorously proved and also illustrated through examples.