Variable fractional-delay filter design using weighted-least-squares singular-value decomposition

This paper proposes a weighted-least-squares singular-value-decomposition (WLS-SVD) method and shows that the problem of designing 1D variable fractional-delay (VFD) digital filter can be elegantly reduced to the easier sub-problems that involve 1D constant filter designs and 1D polynomial approximations. By utilizing the WLS-SVD of the variable design specification, we prove that both 1D constant filters and 1D polynomials possess either symmetry or antisymmetry simultaneously. Therefore, a VFD filter can be efficiently obtained by designing 1D constant filters with symmetric or antisymmetric coefficients and performing 1D symmetric or antisymmetric polynomial approximations. Our computer simulations have shown that the WLS-SVD design can achieve much higher design accuracy with significantly reduced filter complexity than the existing WLS design method.