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 one-dimensional (1-D) variable fractional-delay (VFD) digital filter can be elegantly reduced to the easier sub-problems that involve 1-D constant filter designs and 1-D polynomial approximations. By utilizing the WLS-SVD of the variable design specification, we prove that both 1-D constant filters and 1-D polynomials possess either symmetry or anti-symmetry simultaneously. Therefore, a VFD filter can be efficiently obtained by designing 1-D constant filters with symmetric or anti-symmetric coefficients and performing 1-D symmetric or anti-symmetric 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.