Optimal design of maximally flat FIR filters with arbitrary magnitude specifications

An optimal design procedure for maximally flat FIR (finite impulse response) filters, based on the Bernstein polynomial, is proposed. Using a set of recurrence relations, this method simultaneously searches for the optimum order of filter and the orders of tangency at w=0 and w=π, in a staircase-like manner. A detailed comparison to the earlier methods establishes the superiority of this approach. Being an optimal method, it results in the minimum order of the filter required to meet the given specifications. The method is shown to be suitable for the design of this class of filters with arbitrary magnitude specifications for which no method presently exists