Detection of Signals in Noise (eBook)

Anthony D. Whalen (Autor)

Henry G. Booker, Nicholas Declaris (Herausgeber)

eBook Download: PDF

2013 | 1. Auflage
428 Seiten
Elsevier Science (Verlag)
978-1-4832-2054-3 (ISBN)

Infos

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.

Inhalt

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

Produkt-Details

• Erscheint lt. Verlag: 11.9.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Bauwesen
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4832-2054-0 / 1483220540
• ISBN-13: 978-1-4832-2054-3 / 9781483220543