Detection of Signals in Noise
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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.
Table of Contents
Contents
Preface
Acknowledgements
Chapter 1. Probability
1.1 Probability in Brief
1.2 Conditional Probability and Statistical Independence
1.3 Probability Distribution Functions
1.4 Continuous Random Variables
1.5 Functions of Random Variables
1.6 Characteristic Functions
1.7 Averages
Exercises
References
Supplementary Bibliography
Chapter 2. Random Processes
2.1 Introduction
2.2 Relation to Probability
2.3 Ensemble Correlation Functions
2.4 Time Averages
2.5 Time Correlation Functions
2.6 Power Spectral Density
2.7 Response of Linear Filters
Exercises
References
Supplementary Bibliography
Chapter 3. Narrowband Signals
3.1 Introduction
3.2 Deterministic Signal
3.3 Hilbert Transform
3.4 Signal Preenvelope
3.5 Narrowband Filters
3.6 Narrowband Processes
3.7 Fourier Series Representation
Exercises
References
Supplementary Bibliography
Chapter 4. Gaussian Derived Processes
4.1 Gaussian Properties
4.2 Sum of a Sine Wave and a Gaussian Process
4.3 Distribution of the Envelope of a Narrowband Gaussian Process
4.4 Envelope of a Sine Wave Plus Narrowband Noise
4.5 Envelope Squared of Narrowband Process
4.6 Chi-Squared Distribution
4.7 Envelope Squared of a Sine Wave Plus a Narrowband Process
4.8 Noncentral Chi-Squared Distribution
Exercises
References
Supplementary Bibliography
Chapter 5. Hypothesis Testing
5.1 Introduction
5.2 Hypothesis Testing
5.3 Bayes Criterion
5.4 Minimum Error Probability Criterion
5.5 Neyman-Pearson Criterion
5.6 Minimax Criterion
5.7 Multiple Measurements
5.8 Multiple Alternative Hypothesis Testing
5.9 Composite Hypothesis Testing
5.10 Unknown A Priori Information
Exercises
References
Supplementary Bibliography
Chapter 6. Detection of Known Signals
6.1 Introduction
6.2 A Binary Communication System
6.3 The Likelihood Functions
6.4 Matched Filters
6.5 An M-ary Communication System
6.6 Sampled Approach
Exercises
References
Supplementary Bibliography
Chapter 7. Detection of Signals with Random Parameters
7.1 Introduction
7.2 Signals with Random Phase
7.3 The Quadrature Receiver and Equivalent Forms
7.4 Receiver Operating Characteristics
7.5 Signals with Random Phase and Amplitude
7.6 Noncoherent Frequency Shift Keying
7.7 Signals with Random Frequency
7.8 Signals with Random Time of Arrival
7.9 Random Frequency and Time of Arrival
7.10 Sampled Approach
Exercises
References
Supplementary Bibliography
Chapter 8. Multiple Pulse Detection of Signals
8.1 Introduction
8.2 Known Signals
8.3 Signals with Random Parameters
8.4 Diversity
Exercises
References
Supplementary Bibliography
Chapter 9. Detection of Signals in Colored Gaussian Noise
9.1 Introduction
9.2 Karhunen-Loeve Expansion
9.3 Detection of Known Signals
9.4 Receiver Performance
9.5 Optimum Signal Waveform
9.6 The Likelihood Functions
9.7 Integral Equations
9.8 Detection of Signals with Unknown Phase
Exercises
References
Supplementary Bibliography
Chapter 10. Estimation of Signal Parameters
10.1 Introduction
10.2 Bayes Estimate
10.3 Maximum A Posteriori Estimate
10.4 Maximum-Likelihood Estimates
10.5 Properties of Estimators
10.6 Estimation in Presence of White Noise
10.7 Estimation of Specific Parameters
10.8 Estimation in Nonwhite Gaussian Noise
10.9 Generalized Likelihood Ratio Detection
Exercises
References
Supplementary Bibliography
Chapter 11. Extensions Using Matrix Formulation
11.1 Introduction
11.2 Matrix Preliminaries
11.3 Multivariate Complex Gaussian Distribution
11.4 Estimation
11.5 Best Linear Estimator
11.6 Maximum Likelihood Estimation
11.7 Maximum A Posteriori Estimation
11.8 Detection
11.9 Gaussian Signal in Gaussian Noise
11.10 Space-Time Processing
Exercises
References
Supplementary Bibliography
Index
Product details
- No. of pages: 428
- Language: English
- Copyright: © Academic Press 1971
- Published: May 28, 1971
- Imprint: Academic Press
- eBook ISBN: 9781483220543