Low-pass maximally flat IIR digital differentiator design with arbitrary flatness degree

Digital differentiators are often used to estimate the derivative of measured signal. They are realized as FIR (Finite Impulse Response) or IIR (Infinite Impulse Response) digital filters. Low-pass maximally flat differentiators have smooth frequency response and are useful since it can avoid signal distortion caused by ripple in the passband of the differentiator. However, the conventional design method of low-pass maximally flat IIR digital differentiator is limited for flatness degree. Hence this paper proposes a design method for low-pass maximally flat IIR digital differentiators with arbitrary flatness degree. At first, the proposed method formulates the simultaneous equations to derive the coefficients of denominator. Then, the recurrence formula is formulated to derive the coefficients of numerator. Through design examples, it is shown that the proposed method can treat arbitrary flatness degree.