### Spie Press Book

Field Guide to Probability, Random Processes, and Random Data AnalysisFormat | Member Price | Non-Member Price |
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Book Description

Mathematical theory developed in basic courses in engineering and science usually involves deterministic phenomena, and such is the case in solving a differential equation that describes some linear system where both the input and output are deterministic quantities. In practice, however, the input to a linear system, like an imaging system or radar system, may contain a "random" quantity that yields uncertainty about the output. Such systems must be treated by probabilistic methods rather than deterministic methods. For this reason, probability theory and random process theory have become indispensable tools in the mathematical analysis of these kinds of engineering systems. Topics included in this Field Guide are basic probability theory, random processes, random fields, and random data analysis.

Book Details

Table of Contents

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- Preface
- Glossary of Symbols and Notation
- Probability: One Random Variable
- Terms and Axioms
- Random Variables and Cumulative Distribution
- Probability Density Function
- Expected Value: Moments
- Example: Expected Value
- Expected Value: Characteristic Function
- Gaussian or Normal Distribution
- Other Examples of PDFs: Continuous r.v.
- Other Examples of PDFs: Discrete r.v.
- Chebyshev Inequality
- Law of Large Numbers
- Functions of One Random Variable
- Example: Square-Law Device
- Example: Half-Wave Rectifier
- Conditional Probabilities
- Conditional Probability: Independent Events
- Conditional CDF and PDF
- Expected Values
- Example: Conditional Expected Value
- Probability: Two Random Variables
- Joint and Marginal Cumulative Distributions
- Joint and Marginal Density Functions
- Conditional Distributions and Density Functions
- Example: Conditional PDF
- Principle of Maximum Likelihood
- Independent Random Variables
- Expected Value: Moments
- Example: Expected Value
- Bivariate Gaussian Distribution
- Example: Rician Distribution
- Functions of Two Random Variables
- Sum of Two Random Variables
- Product and Quotient of Two Random Variables
- Conditional Expectations and Mean-Square Estimation
- Sums of
*N*Complex Random Variables - Central Limit Theorem
- Central Limit Theorem Example
- Phases Uniformly Distributed on (-π, π)
- Phases Not Uniformly Distributed on (-π, π)
- Example: Phases Uniformly Distributed on (-α, α)
- Central Limit Theorem Does Not Apply
- Example: Non-Gaussian Limit
- Random Processes
- Random Processes Terminology
- First- and Second-Order Statistics
- Stationary Random Processes
- Autocorrelation and Autocovariance Functions
- Wide-Sense Stationary Process
- Example: Correlation and PDF
- Time Averages and Ergodicity
- Structure Functions
- Cross-Correlation and Cross-Covariance Functions
- Power Spectral Density (PSD)
- Example: Power Spectral Density
- PSD Estimation
- Bivariate Gaussian Processes
- Multivariate Gaussian Processes
- Examples of Covariance Function and PSD
- Interpretations of Statistical Averages
- Random Fields
- Random Fields Terminology
- Mean and Spatial Covariance Functions
- 1-D and 3-D Spatial Power Spectrums
- 2-D Spatial Power Spectrum
- Structure Functions
- Example: Power Spectral Density
- Transformations of Random Processes
- Memoryless Nonlinear Transformations
- Linear Systems
- Expected Values of a Linear System
- Example: White Noise
- Detection Devices
- Zero-Crossing Problem
- Random Data Analysis
- Tests for Stationarity, Periodicity, and Normality
- Nonstationary Data Analysis for Mean
- Analysis for Single Time Record
- Runs Test for Stationarity
- Bibliography
- Index

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