The low delay low-pass FIR digital differentiators having flat passband and equiripple stopband

The low-pass maximally flat FIR digital differentiator (low-pass MFDD) provides high accurate differentiation around the frequency ω = 0, while it reduces noises in the high frequency. Recently, authors proposed the low delay low-pass MFDD, but it can not get the steep cutoff characteristic. This paper proposes a design method of the low delay low-pass FIR digital differentiators having the flat passband and the equiripple stopband. The proposed transfer function is consist of the passband function and the stopband function. The passband function realizes the high accurate differentiation and the desired delay at ω = 0. The stopband function provides arbitrary roots in the stopband. Those roots are updated to be the optimal ones by using Remez algorithm iteratively.