# Detection of Signals in Noise

1st Edition - May 28, 1971

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• Author: Anthony D. Whalen
• eBook ISBN: 9781483220543

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## Description

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.

• 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

7.5 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

9.5 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
• Published: May 28, 1971
• eBook ISBN: 9781483220543