Engineering

My Instructor Resource Center : Log in or request access

Probability and Random Processes with Applications to Signal Processing, 3/E
Henry Stark, Illinois Institute of Technology
John W. Woods, Rensselaer Polytechnic Institute

ISBN-10: 0130200719
ISBN-13: 9780130200716

Publisher: Prentice Hall
Copyright: 2002
Format: Cloth; 699 pp
Published: 07/24/2001
Status: Instock

Net price: $119.25 (What's this?)

Request a printed exam copy

Email this page to a colleague
Prepare for the First Day of Class
Learn about customization options

For courses in Probability and Random Processes.

This book is a comprehensive treatment of probability and random processes that, more than any other available source, combines rigor with accessibility. Beginning with the fundamentals of probability theory and requiring only college-level calculus, the book develops all the tools needed to understand more advanced topics such as random sequences (Chapter 6), continuous-time random processes (Chapter 7), and statistical signal processing (Chapter 9). The book progresses at a leisurely pace, never assuming more knowledge than contained in the material already covered. Rigor is established by developing all results from the basic axioms (Chapters 1,2) and carefully defining and discussing such advanced notions as stochastic convergence, stochastic integrals and resolution of stochastic processes (Chapter 8). The 3rd Edition has a large number of new topics, not present in the 2nd Edition, including additional material on basic probability (Appendix B, Section 1.8, Section 1.11), statistics (chi-square and Student-t in Section 2.4, Section 4.1), misuses of probability (Sec. 1.3), and signal processing (all of Chapter 9).

NEW - Expository discussions of state-of-the-art computer-oriented techniques—Includes the Expectation-Maximization algorithm (Section 9.4), Hidden Markov Modeling (Section 9.5), high-resolution spectral estimation (Chapter 9.6), and Simulated Annealing (Section 9.7). These algorithms are in use in image processing, speech processing by computer, oil exploration, and a host of other research and commercial applications.
- Exposes students to state-of-the-art stochastic algorithms in preparation for 2nd and 3rd year advanced graduate courses. Most of this material is available only in IEEE journals or specialized books for advanced students. Ex.___

NEW - A large number of worked-out examples in all chapters (Chapters 1-9)—Includes examples that are furnished in the form of Matlab.m files (Examples 4.1-7, 4.1-8, 4.1-9). Also many new end-of-chapter homework problems have been added. These include applications to wireless communications, packet-switched communications, receiver operating characteristics (ROC) curves, medical screening, and politically correct, student-teacher interactions.
- Illustrates the applications of the theory and provides the necessary clues for solving the homework problems. Many of the problems are designed to force the student to go back to the text to review the theory. Also the Matlab examples illustrate how to numerically solve probability-related problems, which do not have closed-form solutions in analytic form. Ex.___

NEW - A new set of reference appendices designed to help the reader understand the developments in the main body of the text—These appendices include a review of the kind of basic math one encounters in elementary probability (Appendix A) including contour integration, and proof-by-induction. Specialized functions of great utility in probability such as the Dirac delta function and the Gamma function are furnished in Appendix B. Functional transformations and Jacobians, often lightly passed-over or omitted altogether in undergraduate math, are reviewed in Appendix C. An introduction to Measure Theory and its relation to probability theory is furnished in Appendix D. The sampling of continuous-time random processes as a means of generating random sequences is furnished in Appendix E. The discussions in these appendices are necessarily brief but contain enough information for the stated purpose.
- Provides the necessary reference material in one source. For the students weak in mathematical preparation, the required material is right there. For the better prepared students, topics such as measure theory and sampling theory are there to enhance his/her study of probability and random processes. Ex.___

NEW - All of the material on random sequences now appears in one chapter (Chapter 6) and the stationary case is treated as a special case of the more general theory. Likewise with continuous-time random processes: all of the material now appears in one chapter (Chapter 7) with the stationary case being treated as a special case of the general theory.
- Makes it much easier for the beginning student in stochastic processes to assimilate the material. Ex.___

NEW - Section on the misuses and paradoxes of probability (Section 1.3)—Abstracts from real-world examples the misuse of probability to create “junk science” and the problem of drawing conclusions from probabilistic data. Examples are taken from legal cases, claims for life on other planets, and medical statistics. Homework problems and worked-out examples dealing with these subjects have been added (Example 1.10-3, HW 1.18, 1.19).
- Makes the students aware of the misuses and paradoxes of probability and also helps him/her relate probability to real life. Ex.___

Expository discussions of state-of-the-art computer-oriented techniques—Includes the Expectation-Maximization algorithm (Section 9.4), Hidden Markov Modeling (Section 9.5), high-resolution spectral estimation (Chapter 9.6), and Simulated Annealing (Section 9.7). These algorithms are in use in image processing, speech processing by computer, oil exploration, and a host of other research and commercial applications.
- Exposes students to state-of-the-art stochastic algorithms in preparation for 2nd and 3rd year advanced graduate courses. Most of this material is available only in IEEE journals or specialized books for advanced students. Ex.___

A large number of worked-out examples in all chapters (Chapters 1-9)—Includes examples that are furnished in the form of Matlab.m files (Examples 4.1-7, 4.1-8, 4.1-9). Also many new end-of-chapter homework problems have been added. These include applications to wireless communications, packet-switched communications, receiver operating characteristics (ROC) curves, medical screening, and politically correct, student-teacher interactions.
- Illustrates the applications of the theory and provides the necessary clues for solving the homework problems. Many of the problems are designed to force the student to go back to the text to review the theory. Also the Matlab examples illustrate how to numerically solve probability-related problems, which do not have closed-form solutions in analytic form. Ex.___

A new set of reference appendices designed to help the reader understand the developments in the main body of the text—These appendices include a review of the kind of basic math one encounters in elementary probability (Appendix A) including contour integration, and proof-by-induction. Specialized functions of great utility in probability such as the Dirac delta function and the Gamma function are furnished in Appendix B. Functional transformations and Jacobians, often lightly passed-over or omitted altogether in undergraduate math, are reviewed in Appendix C. An introduction to Measure Theory and its relation to probability theory is furnished in Appendix D. The sampling of continuous-time random processes as a means of generating random sequences is furnished in Appendix E. The discussions in these appendices are necessarily brief but contain enough information for the stated purpose.
- Provides the necessary reference material in one source. For the students weak in mathematical preparation, the required material is right there. For the better prepared students, topics such as measure theory and sampling theory are there to enhance his/her study of probability and random processes. Ex.___

All of the material on random sequences now appears in one chapter (Chapter 6) and the stationary case is treated as a special case of the more general theory. Likewise with continuous-time random processes: all of the material now appears in one chapter (Chapter 7) with the stationary case being treated as a special case of the general theory.
- Makes it much easier for the beginning student in stochastic processes to assimilate the material. Ex.___

Section on the misuses and paradoxes of probability (Section 1.3)—Abstracts from real-world examples the misuse of probability to create “junk science” and the problem of drawing conclusions from probabilistic data. Examples are taken from legal cases, claims for life on other planets, and medical statistics. Homework problems and worked-out examples dealing with these subjects have been added (Example 1.10-3, HW 1.18, 1.19).
- Makes the students aware of the misuses and paradoxes of probability and also helps him/her relate probability to real life. Ex.___

(NOTE: Each chapter concludes with a Summary, Problems, and References.)

1. Introduction to Probability.

Introduction: Why Study Probability? The Different Kinds of Probability. Misuses, Miscalculations, and Paradoxes in Probability. Sets, Fields, and Events. Axiomatic Definition of Probability. Joint, Conditional, and Total Probabilities; Independence. Bayes' Theorem and Applications. Combinatorics. Bernoulli Trials—Binomial and Multinomial Laws. Asymptotic Behavior of the Binomial Law: The Poisson Law. Normal Approximation to the Binomial Law.

2. Random Variables.

Introduction. Definition of a Random Variable. Probability Distribution Function. Probability Density Function. Continuous, Discrete and Mixed Random Variables. Conditional and Joint Distributions and Densities. Failure Rates.

3. Functions of Random Variables.

Introduction. Solving Problems of the Type Y=g(X). Solving Problems of the Type Z=g(X,Y). Solving Problems of the Type V=g(X,Y), W=h(X,Y). Additional Examples.

4. Expectation and Introduction to Estimation.

Expected Value of a Random Variable. Conditional Expectation. Moments. Chebyshev and Schwarz Inequalities. Moment Generating Functions. Chernoff Bound. Characteristic Functions. Estimators for the Mean and Variance of the Normal Law.

5. Random Vectors and Parameter Estimation.

Joint Distributions and Densities. Multiple Transformation of Random Variables. Expectation Vectors and Covariance Matrices. Properties of Covariance Matrices. Simultaneous Diagonalization of Two Covariance Matrices and Applications in Pattern Recognition. The Multidimensional Gaussian Law. Characteristic Functions of Random Vectors. Parameter Estimation. Estimation of Vector Means and Covariance Matrices. Maximum Likelihood Estimators. Linear Estimation of Vector Parameters.

6. Random Sequences.

Basic Concepts. Basic Principles of Discrete-Time Linear Systems. Random Sequences and Linear Systems. WSS Random Sequence. Markov Random Sequences. Vector Random Sequences and State Equations. Convergence of Random Sequences. Laws of Large Numbers.

7. Random Processes.

Basic Definitions. Some Important Random Processes. Continuous-Time Linear Systems with Random Inputs. Some Useful Classification of Random Processes. Wide-Sense Stationary Processes and LSI Systems. Periodic and Cyclostationary Processes. Vector Processes and State Equations.

8. Advanced Topics in Random Processes.

Mean-Square (m.s.) Calculus. m-s Stochastic Integrals. m-s Stochastic Differential Equations. Ergodicity. Karhunen-Loève Expansion. Representation of Bandlimited and Periodic Processes.

9. Applications to Statistical Signal Processing.

Estimation of Random Variables. Innovation Sequences and Kalman Filtering. Wiener Filter for Random Sequence. Expectation-Maximization Algorithm. Hidden Markov Models (HMM). Spectral Estimation. Simulated Annealing.

Appendices.

Appendix A: Review of Relevant Mathematics.

Basic Mathematics. Continuous Mathematics. Residue Method for Inverse Fourier Transform. Mathematical Induction <091>A-4<093>.

Appendix B: Gamma and Delta Functions.

Gamma Function. Dirac Delta Function.

Appendix C: Functional Transformations and Jacobians.

Introduction. Jacobians for n = 2. Jacobian for General n.

Appendix D: Measure and Probability.

Introduction and Basic Ideas. Application of Measure Theory to Probability.

Appendix E: Sampled Analog Waveforms and Discrete-time Signals.

Probability/Random Processes [CORE TEXTS] (Electrical and Computing Engineering)

Companion Website - Stark, 3/E
Stark & Woods
©2002 | Prentice Hall | On-line Supplement; 0 pp | Instock
ISBN-10: 0130356859 | ISBN-13: 9780130356857

Solutions Manual, 3/E
Stark & Woods
©2002 | Prentice Hall | Paper; 336 pp | Instock
ISBN-10: 0130407879 | ISBN-13: 9780130407870
Suggested retail price: $0.00Net price: $0.00 (What's this?)

Companion Website - Stark, 3/E
Stark & Woods
©2002 | Prentice Hall | On-line Supplement; 0 pp | Instock
ISBN-10: 0130356859 | ISBN-13: 9780130356857

Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students contact your Pearson Higher Education representative.