Design of nonrecursive FIR filters with simultaneously MAXFLAT magnitude and prescribed cutoff frequency

Maximally-flat (MAXFLAT) FIR filter design still has a problem in overcoming the cutoff-frequency error due to approximation of the desired frequency response by some closed-form solution. In order to overcome such a difficulty, this paper describes a new method for the design of nonrecursive FIR filters with simultaneously MAXFLAT magnitude and accurate cutoff frequency. The proposed method provides a general formula to find interpolation coefficients for a new closed-form expression of this filter type, obtained by solving solutions of linear differential equations that are derived from the maximal flatness and cutoff-frequency conditions. In addition, this method efficiently determines the optimal degree of flatness by using a powerful objective error function derived from this closed-form solution, and allows direct and simple computation of the coefficients of the filter with the desired frequency response. The design examples are shown to provide a complete and accurate solution for the design of such filters.