Multi-layered neural networks and Volterra series: The missing link

The similarities and differences between the conventional Volterra series techniques and the neural network approach are discussed. The analysis is done from the point of view of representation capabilities for nonlinear systems, and it is shown that a small neural network can represent high-order nonlinear systems, whereas a very large number of terms are required for an equivalent Volterra series representation. This is shown by means of a series expansion of a neural network. Issues common to the two nonlinear modeling approaches are analyzed