Probability and Information Theory, with Applications to Radar

Electronics and Instrumentation, Second Edition, Volume 3: Probability and Information Theory with Applications to Radar provides information pertinent to the development on research carried out in electronics and applied physics. This book presents the established mathematical techniques that provide the code in which so much of the mathematical theory of electronics and radar is expressed.

Organized into eight chapters, this edition begins with an overview of the geometry of probability distributions in which moments play a significant role. This text then examines the mathematical methods in electronics, which rest to an extraordinary degree upon the methods of time-and-frequency analysis. Other chapters consider the exponential dependence of the number of states on the number of units that immediately suggests a logarithmic measure of capacity. This book discusses as well the threshold of intelligibility that depends on the bandwidth of the transmitted signal. The final chapter deals with the simple applications of direct probabilities to radar theory.

This book is a valuable resource for radar engineers.

Inhalt

Editor's Preface
Author's Prefaces
1 An Introduction to Probability Theory
1.1 The Rules of Probability
1.2 Bernoulli's Theorem
1.3 Moments and Generating Functions
1.4 Convolution
1.5 Events at Random in Time
1.6 Probability Density and the Convolution Integral
1.7 The Delta-Function
1.8 Characteristic Functions and the Normal Distribution
1.9 The Rayleigh Distribution
1.10 Entropy as a Measure of Spread
2 Waveform Analysis and Noise
2.1 The Complex Spectrum of Positive and Negative Frequencies0
2.2 The Rectangular Function and its Spectrum
2.3 Parseval's Theorem
2.4 Sampling Analysis
2.5 Sampling of High-Frequency Waveforms
2.6 Poisson's Formula
2.7 Vector Representation of Waveforms
2.8 Uniform Gaussian Noise
2.9 Complex Representation of Real Waveforms
3 Information Theory
3.1 Hartley's Measure of Information Capacity
3.2 Shannon's Measure of Information Content
3.3 Information Gain
3.4 The Symmetrical Formulation of Information Transfer
3.5 Average Expressions
3.6 The Capacity of a Noisy Communication Channel
3.7 Information-Destroying Processes
3.8 Guesswork
4 The Statistical Problem of Reception
4.1 The Ideal Receiver
4.2 Inverse Probability
4.3 Reception of a Steady Voltage in Gaussian Noise
4.4 Sufficiency and Reversibility
4.5 Correlation Reception
4.6 Signals with Unknown Parameters
4.7 Observation Systems and the a Priori Difficulty
4.8 Reception of High-Frequency Signals
4.9 The Complex Formulation
5 Simple Theory of Radar Reception
5.1 The Measurement of Delay
5.2 Threshold Effects
6.3 Continuous Observation and Filtering
5.4 Signals of Doubtful Strength or Existence
5.5 Detection
5.6 Conclusion
6 The Mathematical Analysis of Radar Information
6.1 Introduction
6.2 Complex Signal and Noise Functions
6.3 Range Accuracy
6.4 Noise Ambiguity
6.5 Information Gain
6.6 Discussion of the Threshold Effect
7 The Transmitted Radar Signal
7.1 Accuracy Resolution and Signal Ambiguity
7.2 Ambiguity in Range and Velocity
7.3 The Gaussian Pulse-Train
7.4 Frequency Modulation
7.5 Conclusion
8 Direct Probabilities
8.1 Introduction
8.2 Errors in Binary Decisions
8.3 Signal-to-Noise Ratio
8.4 Envelope Probabilities
8.5 Coherent Versus Incoherent Integration
References
Index