Davall, P. W. (1975) Applications of statistics in the spectral analysis of time-varying systems. PhD thesis, University of Warwick.

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Abstract

Recent advances in the theory of evolutionary spectral analysis
of time-varying systems has led to a resurgence in the popularity of
frequency domain analysis techniques. Policies for adaptive control
of time-varying systems based on state-space and Liaponov techniques
require an accurate measurement of the system phase variables. Under
inherently noisy conditions, access to the complete system state is
seldom possible, and frequency domain analysis requirinq only input/output measurements has an obvious appeal. The sampling properties
of short-term spectral estimates are of central importance both in
system tracking and in choosing suitable control policies.
Goodman (1957) developed some of the sampling properties
associated with spectral estimates of complex bivariate Gaussian
processes. Akaike (1962-66) extended Goodman's results to multi
input/output linear systems with 'Gaussian input forcing functions.
Both these authors considered the case where the data sequences were
stationary.
This thesis reviews and extends the research of these two
authors with respect to single input/output linear systems.
It is shown that the sampling distributions associated with
spectral estimates of stationary open-loop systems are approximately
valid for a restricted class of non-stationary systems. Two examples
of non-stationary systems are investigated and an adaptive control
technique using input compensation in the frequency domain is
developed on a hydraulic fatigue loading rig. It is shown that
statistical tests developed earlier can successfully identify system variations when estimates are measured in a noisy environment.
The sampling distributions associated with spectral estimates
of closed-loop systems are developed and the results are applied to
the modelling and tracking of the human operator response in a trackinq
task situation, for various input signals.
With regard to future research, it remains to extend the results
for closed-loop systems to the time-varying multi input/output
case. In its full complexity this problem remains intractable but
by considering uncorrelated Gaussian inputs it reduces to determining
the distributions associated with multi-variate complex Gaussian
sequences.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Time-series analysis, Frequency spectra, Gaussian processes, Sampling (Statistics)
Official Date:	January 1975
Dates:	Date Event January 1975 Submitted
Institution:	University of Warwick
Theses Department:	School of Engineering
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Douce, John Leonard
Sponsors:	Science Research Council (Great Britain) (SRC)
Extent:	vi, 403 p.
Language:	eng

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