Abstract
The maximally flat FIR digital differentiators have extremely high accuracy around their center frequency. Especially, when high-accurate differentiation is required in the low frequency, the low-pass maximally flat FIR digital differentiators are very useful. However, the conventional low-pass maximally flat FIR digital differentiators have large delay because of the linear phase property. In this paper, we describe a design method of the low-pass maximally flat FIR digital differentiators with reduced delay. The proposed transfer function is derived as a closed-form solution. The proposed differentiators realize the magnitude response which consists of the flat differentiator band around ω = 0 and the flat stop band around the frequency ω = π. Simultaneously, the proposed differentiators realize reduced delay response. The proposed differentiators can also realize the linear phase response, so that the proposed method includes the conventional design methods of the low-pass maximally flat FIR digital differentiators.
