The Volterra Representation and the Wiener Expansion: Validity and Pitfalls

Volterra and Wiener series provide a general representation for a wide class of nonlinear systems. In this paper we derive rigorous results concerning (a) the conditions under which a nonlinear functional admits a Volterra-like integral representation, (b) the class of systems that admit a Wiener representation and the meaning of such a representation, (c) some sufficient conditions providing a connection between the Volterra-like and the Wiener representations, (d) the mathematical validity of the method of Lee and Schetzen for identifying a nonlinear system.

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