Bogdan R. Kosanovic,
"Signal and System Analysis in Fuzzy Information Space"
http://www.neuronet.pitt.edu/~bogdan/FTP/text.html (WWW)
ftp://ftp.neuronet.pitt.edu/pub/bogdan/text/phd.ps (FTP)
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ABSTRACT:
Signal and System Analysis in Fuzzy Information Space
A general approach to signal and system analysis using fuzzy set theory is
developed. A family of temporal fuzzy sets is constructed to provide for
the unsupervised quantitative and qualitative analysis of dynamic motions.
The observed process generated by a physical system is decomposed into
several hidden processes that coexist at the same time but to different
degrees. Each of the identified processes tends to characterize the
corresponding region of attraction that is modeled by a temporal fuzzy set.
The fuzzy information space is constructed from the activities of hidden
processes, i.e. the membership functions of temporal fuzzy sets. It is shown
that the hidden processes generalize the notion of hidden Markov modeling.
Through the introduction of dynamic fuzzy sets, it is suggested that
signal analysis can be performed in fuzzy information space, instead of raw
signal space, because the motivation is to fit the analysis to the significant
aspects of system dynamics instead of fitting the noise in raw data.
An algorithm for estimation of temporal fuzzy sets is discussed and a dynamic
profile validity functional is proposed that determines an upper bound for a
reasonable number of hidden processes. The simulation results from a class of
quasi-stationary processes are presented to verify the applicability of a
proposed method. Analysis of electroencephalographic signals recorded during
sleep is performed to suggest a way the method can be used on real-world
problems. The theoretical extensions developed in this work are laying the
foundations for a practical approach to analysis of complex systems.
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Enjoy,
Bogdan R. Kosanovic
-- Laboratory for Computational Neuroscience e-mail: bogdan@neuronet.pitt.edu University of Pittsburgh phone: (412) 624-6773 http://www.neuronet.pitt.edu/~bogdan/
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