Volterra series

Summary

A Volterra series writes the output of a nonlinear, time-invariant system with memory as a sum of multiple integrals of the input. The first term is a convolution with an impulse response, as for a linear system. The next terms involve products of two, three or more past values of the input, weighted by kernels of several variables. It plays for nonlinear operators the role that the Taylor series plays for functions. It is used to model and identify nonlinear systems in engineering and biology.