Introducing gravitational-wave data analysis, this is an ideal starting point for researchers entering the field, and researchers currently analyzing data.
Research in this field has grown considerably in recent years due to the commissioning of a world-wide network of large-scale detectors. This network collects a very large amount of data that is currently being analyzed and interpreted. This book introduces researchers entering the field, and researchers currently analyzing the data, to the field of gravitational-wave data analysis. An ideal starting point for studying the issues related to current gravitational-wave research, the book contains detailed derivations of the basic formula related to the detectors' responses and maximum-likelihood detection. These derivations are much more complete and more pedagogical than those found in current research papers, and will enable readers to apply general statistical concepts to the analysis of gravitational-wave signals. It also discusses new ideas on devising the efficient algorithms needed to perform data analysis.
Arvustused
'This book serves as a unique contribution to the field of gravitational-wave data analysis and presents, in a single volume, the astrophysics behind signal production, a summary of important ideas in time-series analysis and statistical testing, and the necessity detector-response relations that allow one to construct a suitable analysis pipeline for gravitational-wave data from scratch.' The Observatory 'This is a good overview of the foundations of gravitational wave data analysis. it makes very pleasant reading for the expert and it is a good place to begin for a student who is not familiar with statistics. General Relativity and Gravitation Journal
Muu info
Introducing gravitational-wave data analysis, this is an ideal starting point for researchers entering the field, and researchers currently analyzing data.
| Preface |
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vii | |
| Notation and conventions |
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x | |
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Overview of the theory of gravitational radiation |
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1 | (25) |
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Linearized general relativity |
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2 | (5) |
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Plane monochromatic gravitational waves |
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7 | (3) |
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Description in the TT coordinate system |
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10 | (3) |
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Description in the observer's proper reference frame |
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13 | (4) |
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Gravitational waves in the curved background |
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17 | (2) |
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Energy-momentum tensor for gravitational waves |
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19 | (1) |
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Generation of gravitational waves and radiation reaction |
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20 | (6) |
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Astrophysical sources of gravitational waves |
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26 | (25) |
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27 | (1) |
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28 | (1) |
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29 | (1) |
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Case study: binary systems |
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30 | (12) |
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Case study: a rotating triaxial ellipsoid |
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42 | (3) |
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Case study: supernova explosion |
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45 | (2) |
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Case study: stochastic background |
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47 | (4) |
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Statistical theory of signal detection |
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51 | (48) |
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52 | (4) |
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56 | (6) |
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62 | (9) |
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The matched filter in Gaussian noise: deterministic signal |
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71 | (5) |
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Estimation of stochastic signals |
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76 | (3) |
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79 | (11) |
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Non-stationary stochastic processes |
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90 | (9) |
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99 | (15) |
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Sample mean and correlation function |
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99 | (2) |
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Power spectrum estimation |
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101 | (6) |
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107 | (2) |
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109 | (2) |
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111 | (3) |
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Responses of detectors to gravitational waves |
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114 | (17) |
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Detectors of gravitational waves |
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114 | (1) |
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Doppler shift between freely falling observers |
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115 | (7) |
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Long-wavelength approximation |
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122 | (2) |
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Responses of the solar-system-based detectors |
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124 | (7) |
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Maximum-likelihood detection in Gaussian noise |
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131 | (61) |
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131 | (19) |
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Case studies: deterministic signals |
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150 | (17) |
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167 | (17) |
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Detection of stochastic signals |
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184 | (8) |
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192 | (20) |
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192 | (5) |
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Grid of templates in the parameter space |
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197 | (4) |
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Numerical algorithms to calculate the F-statistic |
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201 | (7) |
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Analysis of the candidates |
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208 | (4) |
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Appendix A: The chirp waveform |
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212 | (6) |
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Appendix B: Proof of the Neyman---Pearson lemma |
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218 | (3) |
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Appendix C: Detector's beam-pattern functions |
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221 | (8) |
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222 | (3) |
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225 | (4) |
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Appendix D: Response of the LISA detector to an almost monochromatic wave |
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229 | (4) |
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Appendix E: Amplitude parameters of periodic waves |
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233 | (2) |
| References |
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235 | (14) |
| Index |
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249 | |
Piotr Jaranowski is an Associate Professor in the Faculty of Physics at the University of Biaystok, Poland. He has been a visiting scientist at the Max Planck Institute for Gravitational Physics and the Friedrich Schiller University, both in Germany, and the Institut des Hautes Études Scientifiques, France. He currently works in the field of gravitational-wave data analysis and general-relativistic problem of motion. Andrzej Królak is a Professor in the Institute of Mathematics at the Polish Academy of Sciences, Poland. He has twice been awarded the Second Prize by the Gravity Research Foundation (once with Bernard Schutz). He has been a visiting scientist at the Max Planck Institute for Gravitational Physics, Germany, and the Jet Propulsion Laboratory, USA. His field of research is gravitational-wave theory data analysis and general theory of relativity, and the phenomena predicted by this theory such as black holes and gravitational waves.
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