Fir band-pass digital differentiators with flat passband and equiripple stopband characteristics

Maximally flat digital differentiators are widely used as narrow-band digital differentiators because of their high accuracy around their center frequency of flat property. To obtain highly accurate differentiation over narrow-band, it is important to avoid the undesirable amplification of noise. In this paper, we introduce a design method of linear phase FIR band-pass differentiators with flat passband and equiripple stopband characteristics. The center frequency at the passband of the designed differentiators can be adjusted arbitrarily. Moreover, the proposed transfer function consists of two functions, i.e. the passband function and the stopband one. The weighting coefficients of the passband function are derived using a closed-form formula based on Jacobi Polynomial. The weighting coefficients of the stopband function are achieved using Remez algorithm.