A Low Complexity Algorithm for Calculating Variable Fractional Delay Filter Coefficients

An algorithm based on least squares and polynomial fitting is proposed, which solves coefficients of the variable fractional delay filter with low complexity in wideband digital beamforming. Firstly, the filter coefficients are calculated by the least squares method in conditions with different amounts of delay and the same passband. Then, the fitted polynomials of the filter coefficients at different delay amounts are derived using the polynomial fitting. Finally, the coefficients of the variable fractional delay filter based on the Farrow are calculated. The simulation results show that the normalized root mean square of the Farrow structure variable fractional delay filter is 4.
$35\times 10^{-5}$
, the maximum magnitude error is -109.41 dB, and the maximum group delay error is 2.
$62\times 10^{-5}$
times the sampling gap. Therefore, while keeping the accuracy of group delay, it can avoid mathematical operations such as partial derivatives and double integrals. The design efficiency of the Farrow structure with variable fractional delay filter coefficients is improved.