A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results.<p>
A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure
the noise-contaminated output. Using such periodic inputs, we show that we can formulate the
problem of identification of LPTV systems in the frequency domain. With the help of the discrete
Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification.<p>
In the frequency domain, we show that the input and the output can be related by using the
discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias
components. A lower bound on the mean square error (MSE) of the estimated alias components
is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is
designed subsequently. The algorithm is extended to the identification of infinite impulse response
(IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the
efficiency of the optimal training signal design.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:SSU.etd-09022009-125409 |
| Date | 10 September 2009 |
| Creators | Yin, Wutao |
| Contributors | Wu, Fang-Xiang, Faried, Sherif O., Saadat Mehr, Aryan, Burton, Richard T. |
| Publisher | University of Saskatchewan |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://library.usask.ca/theses/available/etd-09022009-125409/ |
| Rights | unrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Saskatchewan or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. |
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