Farrow Structures Using Different Transformation Matrices

The direction implementation of Lagrange-type variable fractional-delay (VFD) digital filters does not lead to a Farrow structure with linear-phase subfilters. This paper revisits the existing transformation matrix for transforming the odd-order Lagrange-type VFD filter into a Farrow structure and shows the frequency response errors after the transformation. Then, the results using a new transformation matrix are shown to verify that the odd-order Lagrange-type VFD digital filters can be successfully transformed into a new Farrow structure whose subfilters are linear-phase so that the number of multiplications can almost be reduced by 50%, which speeds up the VFD filtering process and saves the storage cost for the subfilter coefficients. Through exploiting the coefficient-symmetries, a significant reduction of computational complexity can be achieved.