Statistical Theory of Signal Detection

Preface to Second Edition

From the Preface to First Edition

I. Signals And Filters

1. Signals and Their Spectra

2. Filters

3. Narrowband Signals

4. Narrowband Filters

5. The Uncertainty Relation

6. The Synthesis of Filters

Problems

Bibliography

II. Noise

1. Stochastic Processes and Their Distributions

2. The Spectral Density

3. Two Varieties of Noise

4. Gaussian Stochastic Processes

5. The Physics of Noise

6. Narrowband Noise

Problems

Bibliography

III. Hypothesis Testing

1. Signal Detection and Statistics

2. Testing of Simple Hypotheses by a Single Measurement

3. Testing of Simple Hypotheses by Multiple Measurements

Problems

Bibliography

IV. Detection of a Known Signal

1. Detection in White Gaussian Noise

2. The Matched Filter

3. Detection in Colored Noise

4. The Karhunen—Loeve Expansion

5. Solution of the integral Equations

Problems

Bibliography

V. Detection of Signals of Unknown Phase

1. Testing Composite Hypotheses

2. Detection of a Signal of Unknown Phase

3. The Detectability of Signals of Unknown Phase

4. Detection of Signals of Unknown Amplitude and Phase

5. Signals of Unknown Amplitude, Phase, and Time of Arrival

Problems

Bibliography

VI. Digital Communications

1. The Transmission of Discrete Information

2. Binary Channels

3. Channels with More than Two Signals

4. The Reception of Overlapping Pulses

Problems

Bibliography

VII. Detection by Multiple Observations

1. Detection of a Fixed Number of Signals

2. Detection Probability of the Quadratic Threshold Detector

3. Sequential Detection

Problems

Bibliography

VIII. The Estimation of Signal Parameters

1. The Theory of Estimation

2. Estimating Signal Parameters

3. Estimation of Signal Arrival Time

4. Estimation of Signal Arrival Time and Carrier Frequency

Problems

Bibliography

IX. Detection of Signals with Unknown Parameters

1. Maximum-likelihood Detection

2. Detection of a Signal of Unknown Arrival Time

3. Detection of a Signal of Unknown Arrival Time and Carrier Frequency

4. Non-parametric Detection

Problems

Bibliography

X. Signal Resolution

1. The Specification of Receivers

2. The Specification of Signals

3. The Detection of Signals in Clutter

Problems

Bibliography

XI. Stochastic Signals

1. The Structure of the Receiver

2. The Performance of the Receiver

3. Summary

Problems

Bibliography

Appendices

A. Integral Transforms

B. Characteristic Functions

C. The Covariances of Fourier Coefficients of a Random Process

D. The Circular Gaussian Density Function

E. Solution of an integral Equation

F. The Q-Function

G. Error Probability for a Channel with Two Non-orthogonal Signals of Random Phases

Author index

Subject index

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