Volterra series characterisations and identification of nonlinear bioacoustic systems
Volterra series characterisations and identification of nonlinear bioacoustic systems
This thesis is concerned the development of useful engineering techniques for the characterisation and identification of nonlinear systems in terms of their Volterra Series representations.
The Volterra series is presented and discussed in some detail. Various Techniques for deriving a system's Volterra kernels from a differential equation are discussed. An example of the extension of these procedures to distributed parameter systems is given in the form of the Burgers equation or nonlinear acoustic propagation. Mathematical criteria for the convergence of the series are presented and are compared with qualitaitve features of the system's behaviour which are shown to be necessary for convergence. In this way a number of criteria are developed in order to determine under what circumstance the Volterra series is suitable for the modelling of a particularly nonlinear system.
Related functional series are discussed, in particular the Hermite functional series which is considered in a stochastic context. The properties of this series are used to allow an interpretation of a linear frequency response function estimator applied to a nonlinear system.
A newer identification procedure is discussed which involves maximum length sequences. These are reviewed in such a way as to emphasise the important `multiply and shift' property which makes this procedure work. A number of new results are presented which enable the experimenter to efficiently generate and manipulate such sequences. The identification procedure is examined in detail together wiht strategies to enhance its efficiency and reliability and to reduce the phenomenon of overlapping kernel slices. The procedure is tested in simulated data in order to demonstrate its properties.
The same procedure is then used on a number of real nonlinear systems. The first is a small nonlinear amplifier whose second and third Volterra kernels are obtained. The second is the nonlinear path between acoustic stimulation of the human ear and measured otoacoustic (or cochlea) emissions.
University of Southampton
Wright, Matthew Christian Martin
1993
Wright, Matthew Christian Martin
Wright, Matthew Christian Martin
(1993)
Volterra series characterisations and identification of nonlinear bioacoustic systems.
University of Southampton, Doctoral Thesis.
Record type:
Thesis
(Doctoral)
Abstract
This thesis is concerned the development of useful engineering techniques for the characterisation and identification of nonlinear systems in terms of their Volterra Series representations.
The Volterra series is presented and discussed in some detail. Various Techniques for deriving a system's Volterra kernels from a differential equation are discussed. An example of the extension of these procedures to distributed parameter systems is given in the form of the Burgers equation or nonlinear acoustic propagation. Mathematical criteria for the convergence of the series are presented and are compared with qualitaitve features of the system's behaviour which are shown to be necessary for convergence. In this way a number of criteria are developed in order to determine under what circumstance the Volterra series is suitable for the modelling of a particularly nonlinear system.
Related functional series are discussed, in particular the Hermite functional series which is considered in a stochastic context. The properties of this series are used to allow an interpretation of a linear frequency response function estimator applied to a nonlinear system.
A newer identification procedure is discussed which involves maximum length sequences. These are reviewed in such a way as to emphasise the important `multiply and shift' property which makes this procedure work. A number of new results are presented which enable the experimenter to efficiently generate and manipulate such sequences. The identification procedure is examined in detail together wiht strategies to enhance its efficiency and reliability and to reduce the phenomenon of overlapping kernel slices. The procedure is tested in simulated data in order to demonstrate its properties.
The same procedure is then used on a number of real nonlinear systems. The first is a small nonlinear amplifier whose second and third Volterra kernels are obtained. The second is the nonlinear path between acoustic stimulation of the human ear and measured otoacoustic (or cochlea) emissions.
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Published date: 1993
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Local EPrints ID: 462331
URI: http://eprints.soton.ac.uk/id/eprint/462331
PURE UUID: 51c1f6f8-88f4-4f58-b040-3071609b375c
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Date deposited: 04 Jul 2022 19:05
Last modified: 04 Jul 2022 19:05
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Author:
Matthew Christian Martin Wright
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