Coefficients of maximally flat nonrecursive digital filters

A general method is presented for determining the coefficients of maximally flat nonrecursive digital filters. Recursive relations with integer coefficients are derived for these coefficients by explicit calculations imitating Crout's method for solving the linear equations obtained by setting the derivatives of the symmetric, linear phase transfer function to zero at w = 0 and w = π. For a given order of the filter, the amount of computation required in this method is uniformly the same for any combination of permissible degrees of flatness at w = 0 and w = π.