A general expression of the low-pass maximally flat FIR digital differentiators

This paper describes a general expression of the transfer function of the low-pass maximally flat FIR digital differentiator (low-pass MFDD). The low-pass MFDD provides extremely high accurate differentiation around ω = 0. Simultaneously, it can reduce noises in the high frequency. However, the conventional design method of the low-pass MFDD is designed with the linear phase characteristics. By contrast, the proposed method can adjust the value of the group delay at ω = 0, so that the proposed method can realize not only the linear phase characteristics but the low or the high delay characteristics.