LAUSR

The present paper describes a closed-form transfer function of low-delay band-pass maximally flat FIR digital differentiators. Band-pass maximally flat FIR digital differentiators provide extremely high-accuracy differentiation around the center frequency which is adjusted arbitrarily. At the same time, they can reduce noise in the frequency except around the center frequency. However, the conventional method for designing band-pass maximally flat FIR digital differentiators requires linear phase characteristics. In contrast, the proposed method can realize low-delay characteristics as well as linear phase characteristics and, therefore, is a general expression of band-pass maximally flat FIR digital differentiators. The proposed transfer function is achieved as the sum of two maximally flat complex FIR digital differentiators, the coefficients of which are complex conjugates of each other. The transfer functions of these complex differentiators are derived as closed-form solutions, so that the proposed transfer function is also described as a closed-form solution. Through design examples, the effectiveness of the proposed method is confirmed.