Robust structure transformation for causal Lagrange-type variable fractional-delay filters
IEEE Transactions on Circuits and Systems Part I: Regular Papers - Special section on 2008 custom integrated circuits conference (CICC 2008)
Generalized WLS method for designing all-pass variable fractional-delay digital filters
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Hybrid structures for low-complexity variable fractional-delay FIR filters
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Minimax design of low-complexity allpass variable fractional-delay digital filters
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Fractional and nD systems: a continuous case
Multidimensional Systems and Signal Processing
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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 subproblems that involve one-dimensional (1-D) constant filter (subfilter) designs and 1-D polynomial approximations. By utilizing the singular value decomposition (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 symmetrical or antisymmetrical coefficients and performing 1-D symmetrical or antisymmetrical approximations. To perform the weighted-least-squares (WLS) VFD filter design, a new WLS-SVD method is also developed. Moreover, an objective criterion is proposed for selecting appropriate subfilter orders and polynomial degrees. Our computer simulations have shown that the SVD-based design and WLS-SVD design can achieve much higher design accuracy with significantly reduced filter, complexity than the existing WLS design method. Another important part of the paper proposes two new structures for efficiently implementing the resulting VFD filter, which require less computational complexity than the so-called Farrow structure.