Designing high order low delay maximally flat FIR digital differentiators with equiripple stopband

Low delay maximally flat in passband and equiripple in stopband (MFER) FIR Digital Differentiators (DDs) are known to have high differential accuracy with low delay. The transfer function is defined as the subtraction of the stopband function from the passband function. The passband function and the stopband function realizes flatness characteristics and equiripple characteristics, respectively. However, the conventional methods is difficult to design high order low delay low-pass/band-pass MFER FIR DDs. In this article, we propose a design method of high order low delay low-pass/band-pass MFER DDs. In the proposed method, the passband function is chosen as the transfer function of the low delay low-pass/band-pass MF FIR DDs instead of full-band DDs. The stopband function is designed by complex Remez algorithm. Finally, through the several examples, we show that the proposed method can design higher order desired DDs than conventional.