Linear Approximations of Nonlinear FIR Systems for Separable Input Processes
2005 (English)In: Automatica, ISSN 0005-1098, Vol. 41, no 3, 459-473 p.Article in journal (Refereed) Published
Nonlinear systems can be approximated by linear time-invariant (LTI) models in-many ways. Here, LTI models that are optimal approximations in the mean-square error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is presented. This condition says that the in ut should be separable of a certain order, i.e., that certain conditional expectations should be,P linear. For the special case of Gaussian input signals, this condition is closely related to a generalized version of Bussgang's classic theorem about static nonlinearities. It is shown that this generalized theorem can be used for structure identification and for the identification of generalized Wiener-Hammerstein systems.
Place, publisher, year, edition, pages
Elsevier, 2005. Vol. 41, no 3, 459-473 p.
System identification, Mean-square error, Nonlinear systems, Linearization
IdentifiersURN: urn:nbn:se:liu:diva-46142DOI: 10.1016/j.automatica.2004.11.016OAI: oai:DiVA.org:liu-46142DiVA: diva2:267038
© 2004 Elsevier Ltd. All rights reserved.2009-10-112009-10-112013-07-17