Design of IIR full-band differentiators with improved nearly linear phase

Abstract

Linear, or almost linear phase in the design of digital differentiators depends both on the method of calculation of the filter coefficients and the adopted structural design. Acknowledging the importance of this design objective, we developed a method to derive infinite impulse response differentiators which tackles it from both perspectives and yields improved characteristics compared to our previous design. We have replaced the differentiator structure comprising an all-pass filter and a delay line with a configuration of two infinite impulse response all-pass filters. Furthermore, we provide a procedure for determining an improved initial solution to the optimization of filter coefficients, as well as a procedure for improving the differentiator's magnitude response. The final solution exhibits considerably lower error at low frequencies and is thus suitable for the common scenario where the relevant spectral content decreases with frequency. The proposed filters of third and fifth order outperform many existing solutions in literature, especially in terms of the phase characteristic and time-domain performance.