A new approach to the design of nearly linear-phase infinite impulse response fullband differentiators is discussed in this paper. Transfer function of these differentiators is expressed as the product of a \(\left( 1-z^{-1}\right)\) term, a minimum-phase function, and an all-pass transfer function, whose coefficients are determined by minimizing the Chebyshev norms of relative magnitude and phase response linearity errors. Design examples demonstrate that proposed second- and third-order minimum-phase differentiators can have relative magnitude response errors below 1% and 0.25%, respectively. Additionally, the maximum phase response linearity error of the proposed differentiators decreases as the order of the corresponding all-pass filter increases, while being less than 5.1 and 2.9 degrees in the case of the first- and second-order all-pass filters, respectively. A comparison with existing infinite impulse response fullband differentiators reveals that proposed differentiators can achieve lower phase and magnitude response errors, while requiring less multiplications for realization.
