Balmer, Leslie (1986) Short term spectral estimation with applications. PhD thesis, University of Warwick.

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Abstract

This thesis investigates the effect of finite record length on spectral estimation with particular reference to the estimation of frequency response functions and to the application of frequency response methods to the problem of adaptive control.

Conventional analysis of the statistics of frequency response estimation has concentrated on the statistics of the auto and cross spectral estimates involved. The approach adopted here is to attribute the errors in the estimates to transient terms caused by the finite record lengths of input and output data. It is shown that these transient terms can be separated into a term correlated with the input and an uncorrelated term. The first term causes bias and the second can be regarded as an uncorrelated external disturbance.

Expressions for the bias of the estimate are obtained both in open-loop and closed-loop configurations. An expression for the variance of the estimator is obtained for the open-loop case only, but confidence intervals on the estimates are derived by both configurations.

A new parametric method of identification is investigated, the novelty being in the introduction of additional parameters to account for the transient terms. It is shown that the bias due to the finite record length can be removed completely in the noise free case. Methods similar to those used for parametric identification in the time domain are used to reduce the bias when noise is present.

Results obtained for non-parametric and parametric identification are applied to the area of adaptive control.

Methods of applying frequency domain techniques to the problem of adaptive control are investigated. It is shown that in certain areas such an approach can have advantages over the corresponding time domain methods.

The results obtained, both in the area of frequency response estimation and in the field of adaptive control, are verified by simulation studies.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics Q Science > QC Physics T Technology > TA Engineering (General). Civil engineering (General) T Technology > TJ Mechanical engineering and machinery
Library of Congress Subject Headings (LCSH):	Power spectra, Estimation theory, Frequency spectra, Adaptive control systems
Official Date:	April 1986
Dates:	Date Event April 1986 Submitted
Institution:	University of Warwick
Theses Department:	Department of Engineering
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Douce, J. L.
Sponsors:	Science and Engineering Research Council (Great Britain)
Extent:	1 volume (various pagings) : illustrations, charts
Language:	eng

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