Real-time integration and differentiation of analog signals by means of digital filtering

A novel filter design method for broadband recursive digital integrators and differentiators is presented. The performance of the digital infinite-impulse response (IIR) filters designed with the method is compared with that of finite-impulse response (FIR) filters and that of classical numerical integration and differentiation. The common conviction that IIR filters with excellent amplitude characteristics always have poor phase behavior is refuted. It is shown that it is possible to design easily realizable IIR integrators and differentiators with an arbitrarily small amplitude and phase error. While there is no FIR alternative for IIR integrators, both FIR and IIR methods give competitive results for differentiators