Whalen / Booker / Declaris Detection of Signals in Noise

1. Auflage 2013
ISBN: 978-1-4832-2054-3
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 428 Seiten, Web PDF

Detection of Signals in Noise serves as an introduction to the principles and applications of the statistical theory of signal detection. The book discusses probability and random processes; narrowband signals, their complex representation, and their properties described with the aid of the Hilbert transform; and Gaussian-derived processes. The text also describes the application of hypothesis testing for the detection of signals and the fundamentals required for statistical detection of signals in noise. Problem exercises, references, and a supplementary bibliography are included after each chapter. Students taking a graduate course in signal detection theory.

Autoren/Hrsg.

Whalen, Anthony D.

Booker, Henry G.

Declaris, Nicholas

Inhaltsverzeichnis

1;Front Cover
;1
2;Detection of Signals in Noise
;4
3;Copyright Page
;5
4;Table of Contents
;6
5;Preface;10
6;Acknowledgments
;12
7;Chapter 1. Probability
;16
7.1;1.1 Probability in Brief;16
7.2;1.2 Conditional Probability and Statistical Independence;17
7.3;1.3 Probability Distribution Functions
;18
7.4;1.4 Continuous Random Variables;19
7.5;1.5 Functions of Random Variables;23
7.6;1.6 Characteristic Functions;29
7.7;1.7 Averages;32
7.8;Exercises;37
7.9;References;41
7.10;SUPPLEMENTARY BIBLIOGRAPHY;41
8;Chapter 2. Random Processes
;42
8.1;2.1 Introduction;42
8.2;2.2 Relation to Probability;43
8.3;2.3 Ensemble Correlation Functions;45
8.4;2.4 Time Averages;51
8.5;2.5 Time Correlation Functions;54
8.6;2.6 Power Spectral Density;54
8.7;2.7 Response of Linear Filters;59
8.8;Exercises;66
8.9;References;69
8.10;SUPPLEMENTARY BIBLIOGRAPHY;69
9;Chapter 3. Narrowband Signals
;70
9.1;3.1 Introduction;70
9.2;3.2 Deterministic Signal;71
9.3;3.3 Hilbert Transform;76
9.4;3.4 Signal Preenvelope;84
9.5;3.5 Narrowband Filters;85
9.6;3.6 Narrowband Processes;90
9.7;3.7 Fourier Series Representation;93
9.8;Exercises;98
9.9;References;100
9.10;SUPPLEMENTARY BIBLIOGRAPHY;100
10;Chapter 4. Gaussian Derived Processes
;102
10.1;4.1 Gaussian Properties;102
10.2;4.2 Sum of a Sine Wave and a Gaussian Process;114
10.3;4.3 Distribution of the Envelope of a Narrowband Gaussian Process;116
10.4;4.4 Envelope of a Sine Wave Plus Narrowband Noise;118
10.5;4.5 Envelope Squared of Narrowband Process;123
10.6;4.6 Chi-Squared Distribution;124
10.7;4.7 Envelope Squared of a Sine Wave Plus a Narrowband Process;127
10.8;4.8 Noncentral Chi-Squared Distribution;128
10.9;Exercises;133
10.10;References;137
10.11;SUPPLEMENTARY BIBLIOGRAPHY;138
11;Chapter 5. Hypothesis Testing
;140
11.1;5.1 Introduction;140
11.2;5.2 Hypothesis Testing;141
11.3;5.3 Bayes Criterion;145
11.4;5.4 Minimum Error Probability Criterion;147
11.5;5.5 Neyman-Pearson Criterion;147
11.6;5.6 Minimax Criterion;150
11.7;5.7 Multiple Measurements;153
11.8;5.8 Multiple Alternative Hypothesis Testing;155
11.9;5.9 Composite Hypothesis Testing (I)
;158
11.10;5.10 Unknown A Priori Information;161
11.11;Exercises;165
11.12;References;169
11.13;SUPPLEMENTARY BIBLIOGRAPHY;169
12;Chapter 6. Detection of Known Signals
;170
12.1;6.1 Introduction;170
12.2;6.2 A Binary Communication System;171
12.3;6.3 The Likelihood Functions;181
12.4;6.4 Matched Filters;182
12.5;6.5 An M-ary Communication System;194
12.6;6.6 Sampled Approach;198
12.7;Exercises;204
12.8;References;208
12.9;SUPPLEMENTARY BIBLIOGRAPHY;209
13;Chapter 7.
Detection of Signals with Random Parameters;211
13.1;7.1 Introduction;211
13.2;7.2 Signals With Random Phase;211
13.3;7.3 The Quadrature Receiver and Equivalent Forms;215
13.4;7.4 Receiver Operating Characteristics;217
13.5;7.5 Signals With Random Phase and Amplitude;220
13.6;7.6 Noncoherent Frequency Shift Keying;224
13.7;7.7 Signals With Random Frequency;231
13.8;7.8 Signals With Random Time of Arrival;237
13.9;7.9 Random Frequency and Time of Arrival;239
13.10;7.10 Sampled Approach;240
13.11;Exercises;242
13.12;References;250
13.13;SUPPLEMENTARY BIBLIOGRAPHY;251
14;Chapter 8. Multiple Pulse Detection of Signals
;253
14.1;8.1 Introduction;253
14.2;8.2 Known Signals;254
14.3;8.3 Signals With Random Parameters;256
14.4;8.4 Diversity;286
14.5;Exercises;291
14.6;References;296
14.7;SUPPLEMENTARY BIBLIOGRAPHY;297
15;Chapter 9.
Detection of Signals in Colored Gaussian Noise;300
15.1;9.1 Introduction;300
15.2;9.2 Karhunen-Loeve Expansion (1, 2)
;300
15.3;9.3 Detection of Known Signals;305
15.4;9.4 Receiver Performance;310
15.5;9.5 Optimum Signal Waveform;312
15.6;9.6 The Likelihood Functions;314
15.7;9.7 Integral Equations;315
15.8;9.8 Detection of Signals With Unknown Phase;325
15.9;Exercises;331
15.10;References;333
15.11;SUPPLEMENTARY BIBLIOGRAPHY;334
16;Chapter 10. Estimation of Signal Parameters
;336
16.1;10.1 Introduction;336
16.2;10.2 Bayes Estimate;337
16.3;10.3 Maximum A Posteriori Estimate;339
16.4;10.4 Maximum-Likelihood Estimates;339
16.5;10.5 Properties of Estimators;340
16.6;10.6 Estimation in Presence of White Noise;346
16.7;10.7 Estimation of Specific Parameters;349
16.8;10.8 Estimation in Nonwhite Gaussian Noise;363
16.9;10.9 Generalized Likelihood Ratio Detection;367
16.10;Exercises;372
16.11;References;375
16.12;SUPPLEMENTARY BIBLIOGRAPHY;376
17;Chapter 11.
Extensions Using Matrix Formulation;378
17.1;11.1 Introduction;378
17.2;11.2 Matrix Preliminaries;379
17.3;11.3 Multivariate Complex Gaussian Distribution;385
17.4;11.4 Estimation;386
17.5;11.5 Best Linear Estimator;387
17.6;11.6 Maximum Likelihood Estimation;389
17.7;11.7 Maximum A Posteriori Estimation;391
17.8;11.8 Detection;393
17.9;11.9 Gaussian Signal in Gaussian Noise;395
17.10;11.10 Space-Time Processing;398
17.11;Exercises;410
17.12;References;416
17.13;SUPPLEMENTARY BIBLIOGRAPHY;417
18;Index;420