A design method of TYPE IV digital FIR differentiators with maximally flat criterion at an arbitrary frequency

Digital differentiators are widely used to calculate the instantaneous rate of change of sampled signals. One of the design method of them, is using the maximally flat criterion. With the maximally flat criterion, the designed differentiators can have highest accuracy near at the desired frequency ω₀(maximally flat frequency). Recent years, some maximally flat digital FIR differentiators are proposed with closed form formula. But, their method can only choose the maximally flat frequency as ω₀ = 0 or ω₀ = π/2. Furthermore, any conventional proposed can not choose the maximally flat frequency as an arbitrary frequency. In this paper, we introduce a design method of maximally linear differentiators for TYPE IV solution, which can force the magnitude response to be as close to the ideal as possible at an arbitrary frequency. In the same way as the conventional method, the obtained transfer function is represented as closed form formula.