Two Polynomial FIR Filter Structures With Variable Fractional Delay and Phase Shift

This paper introduces two polynomial finite-length impulse response (FIR) digital filter structures with simultaneously variable fractional delay (VFD) and phase shift (VPS). The structures are reconfigurable (adaptable) online without redesign and do not exhibit transients when the VFD and VPS parameters are altered. The structures can be viewed as generalizations of VFD structures in the sense that they offer a VPS in addition to the regular VFD. The overall filters are composed of a number of fixed subfilters and a few variable multipliers whose values are determined by the desired FD and PS values. A systematic design algorithm, based on iteratively reweighted ℓ₁-norm minimization, is proposed. It generates fixed subfilters with many zero-valued coefficients, typically located in the impulse response tails. The paper considers two different structures, referred to as the basic structure and common-subfilters structure, and compares these proposals as well as the existing cascaded VFD and VPS structures, in terms of arithmetic complexity, delay, memory cost, and transients. In general, the common-subfilters structure is superior when all of these aspects are taken into account. Further, the paper shows and exemplifies that the VFDPS filters under consideration can be used for simultaneous resampling and frequency shift of signals.