Recursive wideband digital differentiator and integrator

A new design of a recursive wideband digital differentiator is obtained by optimising the pole-zero locations of existing recursive wideband digital differentiators. Further, a new integrator design is also obtained by inverting the transfer function of the proposed digital differentiator design with suitable modifications. The beauty of these designs is that they are only of second-order recursive systems and have not more than 0.48% relative error in magnitude responses almost over the full Nyquist band, thus being suitable for real-time circuit applications.