Random processes : filtering, estimation and detection

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Title:

Personal Author:

Ludeman, Lonnie C.

Publication Information:

Hoboken, N.J. : Wiley-Interscience, 2003

ISBN:

9780471259756

Subject Term:

Stochastic processes

Signal processing

Image processing

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010019129	QA274 L82 2003	Open Access Book	Book	Searching... Unknown

An understanding of random processes is crucial to many engineering fields-including communication theory, computer vision, and digital signal processing in electrical and computer engineering, and vibrational theory and stress analysis in mechanical engineering. The filtering, estimation, and detection of random processes in noisy environments are critical tasks necessary in the analysis and design of new communications systems and useful signal processing algorithms. Random Processes: Filtering, Estimation, and Detection clearly explains the basics of probability and random processes and details modern detection and estimation theory to accomplish these tasks.
In this book, Lonnie Ludeman, an award-winning authority in digital signal processing, joins the fundamentals of random processes with the standard techniques of linear and nonlinear systems analysis and hypothesis testing to give signal estimation techniques, specify optimum estimation procedures, provide optimum decision rules for classification purposes, and describe performance evaluation definitions and procedures for the resulting methods. The text covers four main, interrelated topics:

* Probability and characterizations of random variables and random processes
* Linear and nonlinear systems with random excitations
* Optimum estimation theory including both the Wiener and Kalman Filters
* Detection theory for both discrete and continuous time measurements

Lucid, thorough, and well-stocked with numerous examples and practice problems that emphasize the concepts discussed, Random Processes: Filtering, Estimation, and Detection is an understandable and useful text ideal as both a self-study guide for professionals in the field and as a core text for graduate students.

Author Notes

Lonnie C. Ludeman is Professor Emeritus of electrical and computer engineering at New Mexico State University.

Preface	p. xv
1 Experiments and Probability	p. 1
1.1 Definition of an Experiment	p. 1
1.2 Combined Experiments	p. 6
1.3 Conditional Probability	p. 20
1.4 Random Points	p. 25
2 Random Variables	p. 37
2.1 Definition of a Random Variable	p. 37
2.2 Common Continuous Random Variables	p. 52
2.3 Common Discrete Random Variables	p. 55
2.4 Transformations of One Random Variable	p. 56
2.5 Computation of Expected Values	p. 66
2.6 Two Random Variables	p. 67
2.7 Two Functions of Two Random Variables	p. 79
2.8 One Function of Two Random Variables	p. 88
2.9 Computation of E[h(X, Y)]	p. 93
2.10 Multiple Random Variables	p. 97
2.11 M Functions of N Random Variables	p. 104
3 Estimation of Random Variables	p. 133
3.1 Estimation of Variables	p. 133
3.2 Linear MMSE Estimation	p. 135
3.3 Nonlinear MMSE Estimation	p. 148
3.4 Properties of Estimators of Random Variables	p. 156
3.5 Bayes Estimation	p. 157
3.6 Estimation of Nonrandom Parameters	p. 164
4 Random Processes	p. 179
4.1 Definition of a Random Process	p. 179
4.2 Characterizations of a Random Process	p. 181
4.3 Stationarity of Random Processes	p. 186
4.4 Examples of Random Processes	p. 188
4.5 Definite Integrals of Random Processes	p. 209
4.6 Joint Characterizations of Random Processes	p. 212
4.7 Gaussian Random Processes	p. 214
4.8 White Random Processes	p. 215
4.9 ARMA Random Processes	p. 216
4.10 Periodic Random Processes	p. 231
4.11 Sampling of Continuous Random Processes	p. 231
4.12 Ergodic Random Processes	p. 232
5 Linear Systems: Random Processes	p. 247
5.1 Introduction	p. 247
5.2 Classification of Systems	p. 247
5.3 Continuous Linear Time-Invariant Systems (Random Inputs)	p. 250
5.4 Continuous Time-Varying Systems with Random Input	p. 258
5.5 Discrete Time-Invariant Linear Systems with Random Inputs	p. 261
5.6 Discrete Time-Varying Linear Systems with Random Inputs	p. 271
5.7 Linear System Identification	p. 273
5.8 Derivatives of Random Processes	p. 273
5.9 Multi-input, Multi-output Linear Systems	p. 274
5.10 Transient in Linear Systems	p. 278
6 Nonlinear Systems: Random Processes	p. 295
6.1 Introduction	p. 295
6.2 Classification of Nonlinear Systems	p. 295
6.3 Random Outputs for Instantaneous Nonlinear Systems	p. 305
6.4 Characterizations for Bilinear Systems	p. 313
6.5 Characterizations for Trilinear Systems	p. 315
6.6 Characterizations for Volterra Nonlinear Systems	p. 316
6.7 Higher-Order Characterizations	p. 318
7 Optimum Linear Filters: The Wiener Approach	p. 335
7.1 Optimum Filter Formulation	p. 335
7.2 Basic Problems	p. 338
7.3 The Wiener Filter	p. 342
7.4 The Discrete Wiener Filter	p. 356
7.5 Optimal Linear System of Parametric Form	p. 364
8 Optimum Linear Systems: The Kalman Approach	p. 383
8.1 Introduction	p. 383
8.2 Discrete Time Systems	p. 384
8.3 Basic Estimation Problem	p. 389
8.4 Optimal Filtered Estimate	p. 392
8.5 Optimal Prediction	p. 401
8.6 Optimal Smoothing	p. 404
8.7 Steady State Equivalence of the Kalman and Wiener Filters	p. 410
9 Detection Theory: Discrete Observation	p. 423
9.1 Basic Detection Problem	p. 423
9.2 Maximum A Posteriori Decision Rule	p. 424
9.3 Minimum Probability of Error Classifier	p. 430
9.4 Bayes Decision Rule	p. 437
9.5 Special Cases for the Multiple-Class Problem (Bayes)	p. 450
9.6 Neyman-Pearson Classifier	p. 455
9.7 General Calculation of Probability of Error	p. 460
9.8 General Gaussian Problem	p. 466
9.9 Composite Hypotheses	p. 490
10 Detection Theory: Continuous Observation	p. 511
10.1 Continuous Observations	p. 511
10.2 Detection of Known Signals in White Gaussian Noise	p. 512
10.3 Detection of Known Signals in Nonwhite Gaussian Noise (ANWGN)	p. 534
10.4 Detection of Known Signals in Combination of White and Nonwhite Gaussian Noise (AW^NWGN)	p. 544
10.5 Optimum Classifier for General Gaussian Processes (Two-Class Detection)	p. 547
10.6 Detection of Known Signals with Random Parameters in Additive White Gaussian Noise	p. 549
Appendixes
Appendix A The Bilateral Laplace Transform	p. 579
Appendix B Table of Binomial Probabilities	p. 587
Appendix C Table of Discrete Random Variables and Properties	p. 591
Appendix D Table of Continuous Random Variables and Properties	p. 593
Appendix E Table for Gaussian Cumulative Distribution Function	p. 595
Index	p. 599

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Author Notes

Table of Contents