Novel digital integrator and differentiator

A novel digital integrator and a novel digital differentiator are presented. Both the integrator and the differentiator are of first order and thus eminently suitable for real-time applications. Both have an almost linear phase. The integrator is obtained by interpolationg two popular digital integration techniques, the rectangular and the trapezoidal rules. The resulting integrator outperforms both the rectangular and the trapezoidal integrators in range and accuracy. The new differentiator is obtained by taking the inverse of the transfer function of the integrator. The effective range of the differentiator is about 0.8 of the Nyquist frequency.