The University of Southampton
University of Southampton Institutional Repository

Nonlinear system analysis by Volterra and Hermite functional expansions

Barrett, J.F. (2012) Nonlinear system analysis by Volterra and Hermite functional expansions, Southampton, GB, University of Southampton, 116pp.

Record type: Book

Abstract

The Volterra series method appeared in systems engineering just after the Second World War and has since been widely used for system modelling. The number of papers using it has grown correspondingly although there are still rather few books on the general theory. The present small book is intended as an initial version of a book treating the subject from a mathematical viewpoint giving importance to clear derivation of results and their mathematical justification. Particular attention is given to the convergence of Volterra series arising from the solution of forced nonlinear differential equations. For Gaussian inputs the book describes, alongside the Volterra theory, also the related Hermite functional expansion which covers general Gaussian inputs as well as white noise. For white noise the Hermite expansion coincides with the Wiener G-functional expansion. The Hermite approach has greater generality than the usual treatment based on Wiener’s theory and using properties of Hermite polynomials has more relation to standard mathematical literature. The Hermite approach also has a certain priority over the Wiener G-functional expansion and is related to that of Itô which also preceded it.

The book originates from an undergraduate course on nonlinear systems given many years ago at Eindhoven Technical High School, now Eindhoven University of Technology. It has been completed in the present form while the writer has been a visitor in the signal processing group of the University of Southampton Institute of Sound and Vibration Research.

PDF NSA.pdf - Other
Download (3MB)

More information

Published date: 20 November 2012
Organisations: Inst. Sound & Vibration Research

Identifiers

Local EPrints ID: 345465
URI: http://eprints.soton.ac.uk/id/eprint/345465
PURE UUID: f5ca76d6-18f8-40eb-9203-9e4bc5edfcd6

Catalogue record

Date deposited: 05 Dec 2012 16:55
Last modified: 18 Jul 2017 05:09

Export record

Contributors

Author: J.F. Barrett

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×