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An algebraic relationship is derived which enables the generalized amplitude dependent describing function to be expressed in terms of the parameters of a general nonlinear integro-differential equation. The algorithm is not restricted to a specific input, but treats the whole class of harmonically related, phase independent, sinusoidal inputs, and is illustrated by a number of examples.

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.

Analytical and graphical methods of interpreting generalised frequency response functions for non-linear systems are derived. It is shown that non-linear phenomena can be classified into intra-kernel and inter-kernel interference and that worst-case responses can be computed. The results are illustrated using several discrete- and continuous-time non-linear systems.

The effects of data pretreatment and mean levels upon nonlinear model structures is investigated. Techniques commmonly used to prefilter data in linear system identification are shown to alter the model structure in the nonlinear case. The effects of mean levels are considered in detail and a new unravelling algorithm is derived to recover the underlying system model when the offsets are external to the system. A new mapping from the time domain to the frequency domain is also introduced for the case where offsets can be considered as an implicit part of the system.