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洋書 | 技術書

Field Guide to Probability, Random Processes, and Random Data Analysis
商品コード: 9780819487018

Field Guide to Probability, Random Processes, and Random Data Analysis

販売価格(税込) 4,830 円
ポイント: 48 Pt
個  数

カゴに入れる

Larry C. Andrews; Ronald L. Phillips
108 pages; Spiral Bound
2012/3/13
FG22

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

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