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Discrete wavelete transform in linear system identification[editovat]

Author: Váňa Zdeněk

Disertační práce 2014

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The thesis presents several approaches to system identification in which wavelet transform is employed for both single and multivariable system identification enabling selection of the particular frequency range of interest. We will show the use of wavelet filters with a property of superior selectivity in frequency domain and having compact support in time domain, which, in turn, influences an accurate implementation. These properties provide the user with possibility of measured data analysis in frequency domain without any loss of information. Consequently, selection of a proper filter allows the user to identify the system on a desired frequency range or to identify a number of systems for distinct frequency ranges. This is specifically convenient for the systems with dominant modes, such as singularly perturbed systems. The possibility of selection of a specific frequency range can be utilized for application-based identification and consequent control, when only a limited frequency range is required. The thesis also provides several points of view on wavelets, what enables the reader to understand both the wavelets and mutual consequences between wavelets and system identification more deeply.

Except of the algorithms described in the thesis, the interconnection of theories of both wavelet transform and system identification is the main contribution of the thesis. Nowadays, there are lot of distinct highly professional tools, which are well-known and widely used by people from some particular branch only. It is therefore very important not only to develop new methods, but also to look for suitable methods across different scientific fields. There is a strong reason for doing it even in situations where no new results can be obtained, since using of tools which are ``new in particular field can always show new analogies and links.

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