Closed-Form Design of Variable Fractional-Delay FIR Filters With Low or Middle Cutoff Frequencies

This paper aims to design variable fractional-delay (VFD) finite-impulse response (FIR) filters with controllable cutoff frequencies. Different with the existing designs, a particular ladder-shaped curve is selected as the desired transfer characteristic of the proposed design. Due to the fact that this particular transfer curve can be well approximated by the convolution windowed spectrum interpolation-based filter, the analytic formula of this filter can be further combined with the cubic spline interpolation and Taylor series expansion, thereby deriving a fast configuration procedure for all tap coefficients in the Farrow structure. Meanwhile, both the fractional delay and the cutoff frequency can be flexibly adjusted by this procedure. By means of theoretical analysis or numerical simulation, we proved that the proposed method is not only suitable to design those VFD FIR filters with low or middle cutoff frequencies, but also concurrently possesses high flexibility in performance adjustment and low complexity in coefficient configuration. Therefore, it is an appropriate supplement of the closed-form WLS design.