Some Advances in the Multitaper Method of Spectrum Estimation
Some Advances in the Multitaper Method of Spectrum Estimation by Kyle Quentin Lepage A thesis submitted to the Department of Mathematics and Statistics in conformity with the requirements for the degree of Doctor of Philosophy Queen’s University Kingston, Ontario, Canada February 2009 Copyright c Kyle Quentin Lepage, 2009 Abstract Four contributions to the multitaper method of applied spectrum estimation are pre- sented. These are a generalization of the multitaper method of spectrum estimation to time-series possessing irregularly spaced samples, a robust spectrum estimate suit- able for cyclostationary, or quasi-cyclostationary time-series, an improvement over the standard, multitaper spectrum estimates using quadratic inverse theory, and finally a method of scan-free spectrum estimation using a rotational shear-interferometer. Each of these topics forms a chapter in this thesis. i Co-Authorship Chapters 2, 3, 4 are co-authored with my supervisor, David J. Thomson. Chapter 5, involving scan-free spectrum estimation with a rotational shear interferometer is co-authored with Shawn Kraut, David J. Brady, and David J. Thomson. The work is a continuation of work begun by David J. Brady, worked on by Shawn Kraut while a post-doctoral researcher at Duke University, and finished by myself and David J. Thomson. ii Acknowledgments I thank David J. Thomson, Shawn Kraut and Mark Halpern for invaluable mentor- ship. I would like to thank Ryan Graham, Karim Rahim, and Azadeh Moghtaderi for numerous enlightening discussions on time-series analysis and statistics, my loving parents Edmond Lepage and Irene Makar, and the rest of the Makar clan for their continual support, and finally my beautiful partner and companion, Elsa Hansen, who has, during these past four years, made the finer things sweeter and the lows not quite as deep.
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