Introduction
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Random Processes
Random Processes.
Optimal Detection Statistic
Optimal Detection Statistic.
Parameter Estimation
Parameter Estimation.
References
Learn how to use Academic’s docs layout for publishing online courses, software documentation, and tutorials.
7.1 Random Processes for Probability Theory 269
- 7.1.1 Power Spectrum
- 7.1.2 Gaussian Noise 273
7.2 Optimal Detection Statistic 275
- 7.2.1 Bayes’s Theorem 275
- 7.2.2 Matched Filter 276
- 7.2.3 Unknown Matched Filter Parameters 277
- 7.2.4 Statistical Properties of the Matched Filter 279
- 7.2.5 Matched Filter with Unknown Arrival Time 281
- 7.2.6 Template Banks of Matched Filters 282
7.3 Parameter Estimation 286
- 7.3.1 Measurement Accuracy 286
- 7.3.2 Systematic Errors in Parameter Estimation 289
- 7.3.3 Confidence Intervals 291
7.4 Detection Statistics for Poorly Modelled Signals 293
- 7.4.1 Excess-Power Method 293
7.5 Detection in Non-Gaussian Noise 295
7.6 Networks of Gravitational-Wave Detectors 298
- 7.6.1 Co-located and Co-aligned Detectors 298
- 7.6.2 General Detector Networks 300
- 7.6.3 Time-Frequency Excess-Power Method for a Network of Detectors
- 7.6.4 Sky Position Localization for Gravitational-Wave Bursts 305
7.7 Data Analysis Methods for Continuous-Wave Sources 307
- 7.7.1 Search for Gravitational Waves from a Known, Isolated Pulsar 309
- 7.7.2 All-Sky Searches for Gravitational Waves from Unknown Pulsars 316
7.8 Data Analysis Methods for Gravitational-Wave Bursts 317
- 7.8.1 Searches for Coalescing Compact Binary Sources 318
- 7.8.2 Searches for Poorly Modelled Burst Sources 332
7.9 Data Analysis Methods for Stochastic Sources 333
- 7.9.1 Stochastic Gravitational-Wave Point Sources 344
Basic Signal Processing
- Signal
- Analog vs. Digital
- Sampling Frequency
- Fourier Transform
- Convolution
- Windowing
- Filtering
- LTI System
- Transfor Function
- Discrete Time Filtering
- Nyquist Sampling Theorem
- Discrete Fourier Transform
- Fast Fourier Transform
- DFT & Discrete Time Convolution
- Digital Filtering
- Digital Filter Design
- Linear Algebra Approach to Signal Processing
- Signal and Vector Space
- Fourier Basis
- Wavelet Basis
- Time-frequency Analysis
- Signal
Appendix Introduction to Signal Processing
- Sampling and Reconstruction
- Discrete-Time Systems
- FIR Filtering and Convolution
- z-Transforms
- Transfer Functions
- Digital Filter Realizations
- Signal Processing Applications
- DFT/FFT Algorithms
- FIR Digital Filter Design
- IIR Digital Filter Design
Appendix Bayesian Inference and Computation
- Markov Chain Monte Carlo
- Model Selection and Nested Sampling
- Assigning Prior Distributions
Appendix Gravitational-Wave Detector Data
- Gravitational-Wave Detector Site Data
- Idealized Initial LIGO Model