Weighted-least-squares design of variable fractional-delay FIR filters using coefficient symmetry

Our previous work has shown that the coefficient symmetry can be efficiently exploited in designing variable finite-impulse-response (FIR) filters with simultaneously tunable magnitude and fractional-delay responses. This paper presents the optimal solutions for the weighted-least-squares (WLS) design of variable fractional-delay (VFD) FIR filters with same-order and different-order subfilters through utilizing the coefficient symmetry along with an imposed coefficient constraint. In deriving the closed-form error functions, since the Taylor series expansions of sin(omega p) and cos(omega p) are used, the numerical integrals using conventional quadrature rules can be completely removed, which speeds up the WLS design and guarantees the optimality of the final solution. Two design examples are given to illustrate that the proposed WLS methods can achieve better design with significantly reduced VFD filter complexity and computational cost than the existing ones including the WLS-SVD approach. Consequently, the proposed WLS design is the best among all the existing WLS methods so far.