Analysis of fast-sampled non-linear systems: Generalised frequency response functions for δδ-operator models

It is widely known that non-linear systems can respond at frequencies other than the excitation frequency. This harmonic distortion must be accommodated when sampling system data for use in identification and can result in high sample frequencies to ensure information about the underlying continuous-time system is not lost. Unfortunately, high sampling rates can have adverse effects on algorithms when used with the absolute-positional operator q  . However, δδ-domain models do not suffer from such problems and are more suited to fast-sampled systems. Therefore, it would appear that the δδ-domain provides a more robust and natural basis for identification and analysis of non-linear systems when fast-sampled data are involved. In this paper a new framework is proposed for analysing polynomial non-linear δδ-domain models in the higher-order transform and frequency domains. The use of the NARMAX approach is advocated and is adapted to cater for non-linear models of the δδ-domain description.