A Novel Variable Fractional Delay Filter Design Using Sparsity Within and Across Groups

The development of Variable Fractional Delay (VFD) FIR filters is essential in the correction of aperture effects for wideband beamforming. However the coefficients controlling these VFDs are rooted in polynomial form, and any attempt to use traditional sparse methods directly on each subfilter may result in untimely delays. To address this complexity, a new structured sparse induction technique is introduced that operates within a weighted least squares (WLS) design framework. By reconverting the original design into a cost function that utilizes a weighted hybrid specification, we efficiently weave together sparsity constraints that apply both to different sets of subfilters and to the system as a whole. The sparse VFDs are then applied to wideband array for beam-squinting compensation. The experimental results show that the proposed design method achieves coefficient sparsity and the minimization of the subfilter orders while ensuring the error accuracy.