Wideband Differentiator and Integrator With Ideal Phase Response

In this paper, we consider the design of a digital differentiator and integrator using the natural logarithm series. The proposed class of differentiators and integrators matches the ideal phase response and the magnitude response as closely as possible at low frequencies for orders lower than those reported in the literature. Furthermore, the bandwidth of the digital differentiator and integrator is extended to cover the entire Nyquist range using a simple multirate technique. In principle, the approach yields the results that are similar to those obtained by the design of fractional order differentiators and integrators.