Describing functions, Volterra series, and the analysis of non-linear systems in the frequency domain

A relationship between the higher-order frequency response functions of the Volterra series model and the well-known describing function representation for non-linear systems is derived. It is shown that a large class of generalized describing functions can be derived from the Volterra model and that this approach removes the restriction to specific inputs. The concept of a worst case transfer function is introduced, and examples are included to illustrate the results.