詳細

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.

Sample Pages(PDF)

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