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Random Processes for Engineers: A Primer [Kõva köide]

(University of South Florida, Tampa, FL, USA)
  • Formaat: Hardback, 195 pages, kõrgus x laius: 234x156 mm, kaal: 540 g, 55 Illustrations, color; 28 Illustrations, black and white
  • Ilmumisaeg: 19-Jan-2017
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1498799035
  • ISBN-13: 9781498799034
Teised raamatud teemal:
  • Formaat: Hardback, 195 pages, kõrgus x laius: 234x156 mm, kaal: 540 g, 55 Illustrations, color; 28 Illustrations, black and white
  • Ilmumisaeg: 19-Jan-2017
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1498799035
  • ISBN-13: 9781498799034
Teised raamatud teemal:
This book offers an intuitive approach to random processes and educates the reader on how to interpret and predict their behavior. Premised on the idea that new techniques are best introduced by specific, low-dimensional examples, the mathematical exposition is easier to comprehend and more enjoyable, and it motivates the subsequent generalizations. It distinguishes between the science of extracting statistical information from raw data--e.g., a time series about which nothing is known a priori--and that of analyzing specific statistical models, such as Bernoulli trials, Poisson queues, ARMA, and Markov processes. The former motivates the concepts of statistical spectral analysis (such as the Wiener-Khintchine theory), and the latter applies and interprets them in specific physical contexts. The formidable Kalman filter is introduced in a simple scalar context, where its basic strategy is transparent, and gradually extended to the full-blown iterative matrix form.

Arvustused

"This is great and timely book! It takes difficult concepts and distills them to the reader in a way that is simple and easy to understand. It connects students with hard to understand theories and concepts though the use of good examples and graphical illustrations." George Edwards, University of Denver, USA

"This book offers an intuitive approach to random processes and discusses how to interpret and predict their behavior. Based on the idea that new techniques are best introduced by specific, low-dimensional examples, the mathematical exposition is made easier to comprehend and serves to motivate the subsequent generalizations. It distinguishes between the science of extracting statistical information from raw data such as a time series about which nothing is known a priori and that of analyzing specific statistical models, such as Bernoulli trials, Poisson queues, ARMA, and Markov processes. The former motivates the concepts of statistical spectral analysis (such as the WienerKhintchine theory), and the latter applies and interprets them in specific physical contexts. The Kalman filter is introduced in a simple scalar context, where its basic strategy is transparent and gradually extended to the full-blown iterative matrix form." IEEE Control Systems Magazine, December 2017 Issue "This is great and timely book! It takes difficult concepts and distills them to the reader in a way that is simple and easy to understand. It connects students with hard to understand theories and concepts though the use of good examples and graphical illustrations." George Edwards, University of Denver, USA

"This book offers an intuitive approach to random processes and discusses how to interpret and predict their behavior. Based on the idea that new techniques are best introduced by specific, low-dimensional examples, the mathematical exposition is made easier to comprehend and serves to motivate the subsequent generalizations. It distinguishes between the science of extracting statistical information from raw data such as a time series about which nothing is known a priori and that of analyzing specific statistical models, such as Bernoulli trials, Poisson queues, ARMA, and Markov processes. The former motivates the concepts of statistical spectral analysis (such as the WienerKhintchine theory), and the latter applies and interprets them in specific physical contexts. The Kalman filter is introduced in a simple scalar context, where its basic strategy is transparent and gradually extended to the full-blown iterative matrix form." IEEE Control Systems Magazine, December 2017 Issue

Preface ix
Author xi
Chapter 1 Probability Basics: A Retrospective
1(54)
1.1 What Is "Probability"?
1(2)
Online Sources
2(1)
1.2 The Additive Law
3(2)
1.3 Conditional Probability and Independence
5(4)
Summary: Important Laws of Probability
8(1)
1.4 Permutations and Combinations
9(1)
1.5 Continuous Random Variables
10(6)
Summary: Important Facts about Continuous Random Variables
15(1)
1.6 Countability and Measure Theory
16(2)
1.7 Moments
18(3)
Summary: Important Facts about Expected Value and Moments
21(1)
1.8 Derived Distributions
21(3)
Summary: Important Facts about Change of Variable
24(1)
1.9 The Normal or Gaussian Distribution
24(4)
Summary: Important Equations Involving the Normal (Gaussian) Distribution
28(1)
1.10 Multivariate Statistics
28(2)
1.11 The Bivariate Probability Density Functions
30(5)
Online Sources
34(1)
Summary: Important Equations for Bivariate Random Variables
35(1)
1.12 The Bivariate Gaussian Distribution
35(4)
Online Sources
38(1)
Summary of Important Equations for the Bivariate Gaussian
39(1)
1.13 Sums of Random Variables
39(5)
Online Sources
43(1)
Summary of Important Equations for Sums of Random Variables
44(1)
1.14 The Multivariate Gaussian
44(2)
1.15 The Importance of the Normal Distribution
46(9)
Exercises
47(8)
Chapter 2 Random Processes
55(20)
2.1 Examples of Random Processes
55(6)
2.2 The Mathematical Characterization of Random Processes
61(6)
Summary: The First and Second Moments of Random Processes
64(3)
2.3 Prediction: The Statistician's Task
67(8)
Exercises
69(6)
Chapter 3 Analysis of Raw Data
75(36)
3.1 Stationarity and Ergodicity
75(2)
3.2 The Limit Concept in Random Processes
77(2)
3.3 Spectral Methods for Obtaining Autocorrelations
79(3)
3.4 Interpretation of the Discrete Time Fourier Transform
82(1)
3.5 The Power Spectral Density
83(6)
3.6 Interpretation of the Power Spectral Density
89(2)
3.7 Engineering the Power Spectral Density
91(4)
3.8 Back to Estimating the Autocorrelation
95(4)
Online Sources
99(1)
3.9 Optional Reading the Secret of Bartlett's Method
99(5)
3.10 Spectral Analysis for Continuous Random Processes
104(7)
Summary: Spectral Properties of Discrete and Continuous Random Processes
105(1)
Exercises
105(6)
Chapter 4 Models for Random Processes
111(40)
4.1 Differential Equations Background
111(1)
4.2 Difference Equations
112(3)
4.3 ARMA Models
115(1)
4.4 The Yule--Walker Equations
116(2)
Online Sources
118(1)
4.5 Construction of ARMA Models
118(1)
4.6 Higher-Order ARMA Processes
119(3)
4.7 The Random Sine Wave
122(3)
Online Sources
124(1)
4.8 The Bernoulli and Binomial Processes
125(3)
Summary: Bernoulli Process
125(1)
Online Sources
126(2)
Summary: Binomial Process
128(1)
4.9 Shot Noise and the Poisson Process
128(8)
Online Sources and Demonstrations
136(1)
4.10 Random Walks and the Wiener Process
136(3)
Online Sources
138(1)
4.11 Markov Processes
139(12)
Online Sources
144(1)
Summary: Common Random Process Models
144(2)
Exercises
146(5)
Chapter 5 Least Mean-Square Error Predictors
151(18)
5.1 The Optimal Constant Predictor
151(1)
5.2 The Optimal Constant-Multiple Predictor
152(1)
5.3 Digression: Orthogonality
152(2)
5.4 Multivariate LMSE Prediction: The Normal Equations
154(2)
5.5 The Bias
156(1)
Online Sources
157(1)
5.6 The Best Straight-Line Predictor
157(2)
5.7 Prediction for a Random Process
159(1)
5.8 Interpolation, Smoothing, Extrapolation, and Back-Prediction
160(1)
5.9 The Wiener Filter
161(8)
Online Sources
166(1)
Exercises
166(3)
Chapter 6 The Kalman Filter
169(24)
6.1 The Basic Kalman Filter
169(2)
6.2 Kalman Filter with Transition: Model and Examples
171(5)
Digression: Examples of the Kalman Model
172(1)
Online Sources
173(3)
6.3 Scalar Kalman Filter with Noiseless Transition
176(1)
6.4 Scalar Kalman Filter with Noisy Transition
177(2)
6.5 Iteration of the Scalar Kalman Filter
179(3)
6.6 Matrix Formulation for the Kalman Filter
182(11)
Online Sources
188(1)
Exercises
189(4)
Index 193
Dr. Arthur David Snider has over fifty years of experience in modeling physical systems in the areas of heat transfer, electromagnetics, microwave circuits, and orbital mechanics, as well as the mathematical areas of numerical analysis, signal processing, differential equations, and optimization. He holds degrees in both mathematics (BS, MIT, PhD, NYU) and physics (MA, Boston U), and he is a registered professional engineer. He served for forty-five years on the faculties of mathematics, physics, and electrical engineering at the University of South Florida after working for five years as a systems analyst at MIT's Draper Instrumentation Lab. He consults in many industries in Florida and has published five other textbooks in applied mathematics.