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Please note that this document contains (a lot of!) copy-righted material that I obtained without the necessary authorizations. This is because I intend these notes for INTERNAL USE ONLY! So, please, distribute it with care. The material presented in Appendix B comes from a course on timing analysis given by Biswajit Paul during the first ASTROSAT Workshop. I really thank Biswajit for letting me use his material and passing me the data files. Document in<strong>format</strong>ion: Author: Mauro Orlandini Revision: 1.34 Last Changed on: 2012/09/10 10:49 LATEX-ed on: 2013/10/15 17:24
Course Outline Table of Contents List of Figures List of Definitions List of Theorems iv vi vii ix I Theory 1 1 Classification of Physical Data 3 1.1 Deterministic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Sinusoidal Periodic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Complex Periodic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.3 Almost-Periodic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Transient Non periodic Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Random Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Stationary Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 Ergodic Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.3 Non stationary Random Processes . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Harmonic Analysis 11 2.1 Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.1.2 Calculation of the Fourier Coefficients . . . . . . . . . . . . . . . . . . . . . 13 2.1.3 Fourier Series and Music . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.4 Fourier Series in Complex Notation . . . . . . . . . . . . . . . . . . . . . . . 16 2.1.5 Theorems and Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1.5.1 Linearity Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1.5.2 The Shifting Rules . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 i
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