SVD-based important theorem for designing variable fractional-delay filters

This paper proves a very important theorem for the singular value decomposition (SVD) of variable fractional-delay (VFD) design specification. We show that the VFD design specification can be decomposed into the outer-products of vectors with mirror-image symmetry or mirror-image anti-symmetry, thus the difficult VFD filter design problem can be reduced to the sub-problems involving constant one-dimensional (1-D) filter designs and 1-D polynomial approximations. Since such sub-problems are much easier to solve than the original VFD filter design, the important theorem provides an elegant way for simplifying the VFD filter design problem as easier sub-problems and leads to an indirect and efficient design approach.