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

The performance of digital infinite impulse response (IIR) integrators and differentiators, calculated by means of a maximum likelihood estimator for transfer functions, is compared with that of their finite impulse response (FIR) counterparts and that of classical numerical integration and differentiation. An original design method that generates stable and reduced-order IIR filters in the complex domain (amplitude as well as phase constraints) is presented. In contrast to common opinion, it is shown that it is possible to design easy realizable IIR integrators and differentiators with an arbitrary small amplitude and phase error. Although there is no FIR alternative for IIR integrators, both FIR and IIR methods give competitive results for differentiators. It is shown that, owing to the design of pure delay filters, the (optimal) fractional delay integrators and differentiators can be used in case the original waveform and one (or more) of its (higher order) derivatives and (or) integrals are required