Fast Generation of Universal Maximally Flat FIR Filters

The relation for impulse response coefficients of Baher's uni- versal maximally flat filters is a threefold summation formula. The sum- mand 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 , the number of zeros , and the group delay parameter . With fixed values for these parame- ters, the total number of additions, multiplications, and divisions required to compute the impulse response coefficients are of the orders , and , respectively. We present a recurrence for the com- putation of for all possible values of under fixed values for and . The recurrence provides speedups of the orders , and for the number of additions, multiplications and divisions, respec- tively.