SVD-based design and new structures for variable fractional-delay filters

This paper 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 (sub-filter) designs and 1-D polynomial approximations. By utilizing the singular value decomposition (SVD) of the variable design specification, 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 symmetrical or anti-symmetrical coefficients and performing 1-D symmetrical or anti-symmetrical polynomial approximations. Moreover, an objective criterion is proposed for selecting appropriate sub-filter orders and polynomial degrees. The design results demonstrate that the SVD-based design approach can achieve higher design accuracy with much less filter complexity than the existing WLS method.