The Volterra series is a model for non-linear behavior similar to the Taylor series. It differs from the Taylor series in its ability to capture "memory" effects. The Taylor series can be used for approximating the response of a nonlinear system to a given input if the output of the system depends strictly on the input at that particular time. In the Volterra series, the output of the nonlinear system depends on the input to the system at all other times. This provides the ability to capture the "memory" effect of devices like capacitors and inductors.
It has been applied in the fields of medicine (biomedical engineering) and biology, especially neuroscience.[1] It is also used in electrical engineering to model intermodulation distortion in many devices, including power amplifiers[2] and frequency mixers.[citation needed] Its main advantage lies in its generalizability: it can represent a wide range of systems. Thus, it is sometimes considered a non-parametric model.
In mathematics, a Volterra series denotes a functional expansion of a dynamic, nonlinear, time-invariant functional. The Volterra series are frequently used in system identification. The Volterra series, which is used to prove the Volterra theorem, is an infinite sum of multidimensional convolutional integrals.