Fast generation of universal maximally flat FIR filters

The relation for impulse response coefficients of Baher´s universal maximally flat filters is a threefold summation formula. The summand involves four binomial coefficients whose computation requires an extensive number of additions and multiplications. There are three main parameters that characterize the filters, the order N, the number of zeros K, and the group delay parameter d. With fixed values for these parameters, the total number of additions, multiplications, and divisions required to compute the impulse response coefficients h_k are of the orders O(N⁴), O(N⁵) and O(N⁴), respectively. We present a recurrence for the computation of h_k for all possible values of K under fixed values for N and d. The recurrence provides speedups of the orders O(N²), O(N³) and O(N²) for the number of additions, multiplications and divisions, respectively.