A Recurrence Formula for Low-Pass Maximally Flat IIR Digital Differentiator Design

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 cased by ripple in the passband of the differentiator. However, the conventional design methods require to formulate and solve a set of linear equations when parameter changes. Hence this paper proposes a novel design method for low-pass maximally flat IIR digital differentiators. The proposed method gives the closed-form frequency response of numerator. On the other hand, the proposed method also gives the recurrence formula to achieve the coefficients of the denominator. Through design examples, the effectiveness of the proposed method is discussed.