Linear Approximations of Nonlinear FIR Systems for Separable Input Processes
2005 (English)Report (Other academic)
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
Linköping: Linköping University Electronic Press, 2005. , 27 p.
LiTH-ISY-R, ISSN 1400-3902 ; 2718
System identification, Mean-square error, Nonlinear systems, Linearization
IdentifiersURN: urn:nbn:se:liu:diva-56074ISRN: LiTH-ISY-R-2718OAI: oai:DiVA.org:liu-56074DiVA: diva2:316865