Detection of Signals in Noise

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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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



    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



    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



    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



    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



    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



    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



    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



    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



    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



    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



    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



    Supplementary Bibliography


Product details

  • No. of pages: 428
  • Language: English
  • Copyright: © Academic Press 1971
  • Published: May 28, 1971
  • Imprint: Academic Press
  • eBook ISBN: 9781483220543

About the Author

Anthony D. Whalen

About the Editors

Henry G. Booker

Nicholas Declaris

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