Recursive Wideband Linear Phase Digital Differentiators and Integrators

New designs of recursive digital differentiator and integrator are obtained by optimizing the pole-zero locations of existing design of recursive digital differentiator over a specific Nyquist band. These obtained designs have not more than 0.37% relative errors in magnitude responses over wideband. Further, the zero-reflection approach is applied to improve the phase responses of proposed and existing recursive digital differentiator and integrator designs. Finally, the obtained recursive digital differentiator and integrator designs of second-order systems have nearly linear phase response almost over the full Nyquist band with preserving the same magnitude response as of the original one. These designs are more suitable for real-time control and signal processing applications.