Identification of linear periodically time-varying (LPTV) systems
Date
2009-08
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
Type
Degree Level
Masters
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.
Description
Keywords
Discrete Fourier Transform, Periodic Input, Mean Square Error, Linear Periodically Time-Vayring Systems, Least-Squares
Citation
Degree
Master of Science (M.Sc.)
Department
Electrical Engineering
Program
Electrical Engineering