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      • HARVEST
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      Identification of linear periodically time-varying (LPTV) systems

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      Date
      2009-08
      Author
      Yin, Wutao
      Type
      Thesis
      Degree Level
      Masters
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      Abstract
      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. 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. 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.
      Degree
      Master of Science (M.Sc.)
      Department
      Electrical Engineering
      Program
      Electrical Engineering
      Supervisor
      Saadat Mehr, Aryan
      Committee
      Wu, Fang-Xiang; Faried, Sherif O.; Burton, Richard T.
      Copyright Date
      August 2009
      URI
      http://hdl.handle.net/10388/etd-09022009-125409
      Subject
      Discrete Fourier Transform
      Periodic Input
      Mean Square Error
      Linear Periodically Time-Vayring Systems
      Least-Squares
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