Probability and Random Processes with Applications to Signal Processing (3rd Edition) (Hardcover)

by Henry Stark (Author), John W. Woods (Author)

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Product Description
(Pearson Education) A rigorous introduction to probability and random processes for engineering students, with applications in signal processing. Features a companion Web site with Matlab codes, multiple choice exams for each chapter, and other materials. Significantly revised from the previous edition: c1993. DLC: Signal processing--Mathematics.

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Preface

The first edition of this book (1986) grew out of a set of notes used by the authors to teach two one-semester courses on probability and random processes at Rensselaer Polytechnic Institute (RPI). At that time the probability course at RPI was required of all students in the Computer and Systems Engineering Program and was a highly recommended elective for students in closely related areas. While many undergraduate students took the course in the junior year, many seniors and first-year graduate students took the course for credit as well. Then, as now, most of the students were engineering students. To serve these students well, we felt that we should be rigorous in introducing fundamental principles while furnishing many opportunities for students to develop their skills at solving problems.

There are many books in this area and they range widely in their coverage and depth. At one extreme are the very rigorous and authoritative books that view probability from the point of view of measure theory and relate probability to rather exotic theorems such as the Radon-Nikodym theorem (see for example Probability and Measure by Patrick Billingsley, Wiley, 1978). At the other extreme are books that usually combine probability and statistics and largely omit underlying theory and the more advanced types of applications of probability. In the middle are the large number of books that combine probability and random processes, largely avoiding a measure theoretic approach, preferring to emphasize the axioms upon which the theory is based. It would be fair to say that our book falls into this latter category. Nevertheless this begs the question: why write or revise another book in this area if there are already several good texts out there that use the same approach and provide roughly the same coverage? Of course back in 1986 there were few books that emphasized the engineering applications of probability and random processes and that integrated the latter into one volume. Now there are several such books.

Both authors have been associated (both as students and faculty) with colleges and universities that have demanding programs in engineering and applied science. Thus their experience and exposure have been to superior students that would not be content with a text that furnished a shallow discussion of probability. At the same time, however, the authors wanted to write a book on probability and random processes for engineering and, applied science students. A measure-theoretic book, or one that avoided the engineering applications of probability and the processing of random signals, was regarded not suitable for such students. At the same time the authors felt that the book should have enough depth so that students taking 2^nd year graduate courses in advanced topics such as estimation and detection, pattern recognition, voice and image processing, networking and queuing, and so forth would not be handicapped by insufficient knowledge of the fundamentals and applications of random phenomena. In a nutshell we tried to write a book that combined rigor with accessibility and had a strong self-teaching orientation. To that end we included a. large number of worked-out examples, MATLAB codes, and special appendices that include a review of the kind of basic math needed for solving problems in probability as well as an introduction to measure theory and its relation to probability. The MATLAB codes, as well as other useful material such as multiple choice exams that cover each of the book's sections, can be found at the book's web site http://www.prenhall.com/stark.

The normal use of this book would be as follows: for a first course in probability at, say the junior or senior year, a reasonable goal is to cover Chapters 1 through 4. Nevertheless we have found that this may be too much for students not well prepared in mathematics. In that case we suggest a load reduction in which combinatorics in Chapter 1 (parts of Section 1.8), failure rates in Chapter 2 (Section 2.7), more advanced density functions and the Poisson transform in Chapter 3 are lightly or not covered the first time around. The proof of the Central Limit Theorem, joint characteristic functions, and Section 4.8, which deals with statistics, all in Chapter 4, can, likewise, also be omitted on a first reading.

Chapters 5 to 9 provide the material for a first course in random processes. Normally such a course is taken in the first year of graduate studies and is required for all further study in signal processing, communications, computer and communication networking, controls, and estimation and detection theory. Here what to cover is given greater latitude. If pressed for time, we suggest that the pattern recognition applications and simultaneous diagonalization of two covariance matrices in Chapter 5 be given lower preference than the other material in that chapter. Chapters 6 and 7 are essential for any course in random processes and the coverage of the topics therein should be given high priority. Chapter 9 on signal processing should, likewise be given high priority, because it illustrates the applications of the theory to current state-of-art problems. However, within Chapter 9, the instructor can choose among a number of applications and need not cover them all if time pressure becomes an issue. Chapter 8 dealing with advanced topics is critically important to the more advanced students, especially those seeking further studies toward the Ph.D. Nevertheless it too can be lightly covered or omitted in a first course if time is the critical factor.

Readers familiar with the 2^nd edition of this book will find significant changes in the 3^rd edition. The changes were the result of numerous suggestions made by lecturers and students alike. To begin with, we modified the title to Probability and Random Processes with Applications to Signal Processing, to better reflect the contents. We removed the two chapters on estimation theory and moved some of this material to other chapters where it naturally fitted in with the material already there. Some of the material on parameter estimation e.g., the Gauss-Markov Theorem has been removed, owing to the need for finding space for new material. In terms of organization, the major changes have been in the random processes part of the book. Many readers preferred seeing discrete-time random phenomena in one chapter and continuous-time phenomena in another chapter. In the earlier editions of the book there was a division along these lines but also a secondary division along the lines of stationary versus non-stationary processes. For some this made the book awkward to teach from. Now all of the material on discrete-time phenomena appears in one chapter (Chapter 6); likewise for continuous-time phenomena (Chapter 7). Another major change is a new Chapter 9 that discusses applications to signal processing. Included are such topics as: the orthogonality principle, Wiener and Kalman filters, The Expectation-Maximization algorithm, Hidden Markov Models, and simulated annealing. Chapter 8 (Advanced Topics) covers much of the same ground as the old Chapter 9 e.g., stochastic continuity, meansquare convergence, Ergodicity etc. and material from the old Chapter 10 on representation of random processes.

There have been significant changes in the first half of the book also. For example, in Chapter 1 there is an added section on the misuses of probability in ordinary life. Here we were helped by the discussions in Steve Pinker's excellent book How the Mind Works (Norton Publishers, New York, 1997). Chapter 2 (Random Variables) now includes discussions 6n more advanced distributions such as the Gamma, Chi-square and the Student-t. All of the chapters have many more worked-out examples as well as more homework problems. Whenever convenient we tried to use MATLAB to obtain graphical results. Also, being a book primarily for engineers, many of the worked-out example and homework problems relate to real-life systems or situations.

We have added several new appendices to provide the necessary background mathematics for certain results in the text and to enrich the reader's understanding of probability. An appendix on Measure Theory falls in the latter category. Among the former are appendices on the delta and gamma functions, probability-related basic math, including the principle of proof-by-induction, Jacobians for n-dimensional transformations, and material on Fourier and Laplace inversion.

For this edition, the authors would like to thank Geoffrey Williamson and Yongyi Yang for numerous insightful discussions and help with some of the MATLAB programs. Also we thank Nikos Galatsanos, Miles Wernick, Geoffrey Chan, Joseph LoCicero, and Don Ucci for helpful suggestions. We also would like to thank the administrations of Illinois Institute of Technology and Rensselaer Polytechnic Institute for their patience and support while this third edition was being prepared. Of course, in the end, it is the reaction of the students that is the strongest driving force for improvements. To all our students and readers we owe a large debt of gratitude.

Henry Stark
John W. Woods

Product Details

• Hardcover: 699 pages
• Publisher: Prentice Hall; 3 edition (August 3, 2001)
• Language: English
• ISBN-10: 0130200719
• ISBN-13: 978-0130200716
• Product Dimensions: 9.3 x 6.6 x 1.1 inches
• Shipping Weight: 2.8 pounds (View shipping rates and policies)
• Average Customer Review: 2.7 out of 5 stars See all reviews (11 customer reviews)
• Amazon.com Sales Rank: #477,640 in Books (See Bestsellers in Books)

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Most Helpful Customer Reviews

11 of 11 people found the following review helpful:

1.0 out of 5 stars Beware: Scattered and full of holes, November 28, 2004

By	T. Bone "mr. gE.E.k" (Boulder, Colorado, USA) - See all my reviews

I had the misfortune to take an EE grad course in Random Processes using this text (3rd edition.) Let me start with the single good point about the book before thrashing its shortcomings. The book does a good job of covering basic probability theory, which is handy if you've never dealt with set theory, algebras, etc. From that point on, it goes downhill quickly. The introduction to random variables and subsequent random process treatment jumps all over the place, skipping many integral pieces and steps along the way. There is no attempt to build a body of knowledge and then instruct the reader in methodology to solve typical problem sets. To compound this, the book is replete with typographical errors in formulas, proofs, and general verbiage. The problem sets at the end of each chapter are sometimes challenging, but mostly just obtuse and vaguely worded exercises that do not follow any progressive order in the chapter just covered. Some of the problem sets actually require knowledge from subsequent chapters to solve, which makes doing the problems more an exercise in leafing forward and backward in the book rather than a meaningful intuition building and problem solving exercise. I will admit that the Papoulis book is a little dense, but it doesn't skip steps or gloss over any 'obvious' steps in the proofs or example problems. It seems that the Schaum's guide and Papoulis books at least follow a progressive process of building knowledge while this book has roughly the same knowledge, but scattered across many chapters (when it logically should all be treated contiguously.) If you happen to take a class using this book, be forewarned that you really will need several other references (Schaum's guide for certain, Papoulis is dense but complete, that's all I have) to piece together the puzzle on this otherwise very interesting and relevant subject.

11 of 11 people found the following review helpful:

2.0 out of 5 stars mediocre Prob and Random Processes textbook, May 29, 2003

By A Customer

I found Probability and Random Processes a difficult subject and it was compounded by the instructor's selection of the stark and woods textbook. While it has some interesting problem sets and the tone of the text is very engaging, Probability and Random Processes, 3rd ed. has several problems. First of all, the book has several typos, including some in derivations which can cause a "what the...?" moment. Second, many sections in the introductory material gloss over derivations, skip steps, or leave proofs of theorems as the classic "exercize for the reader." (!) The biggest problem the text has is that it doesn't adequately explain the intuition for problem solving. For an engineer coming from industry and starting grad school after an extended period away from college, the net result is that the book is not self-contained. I had to buy the Papoulis book and the Schaum's outline to keep my head above water. When the semester was over I ditched the Stark and Woods and kept the Papoulis book.

9 of 9 people found the following review helpful:

3.0 out of 5 stars KooKo, October 29, 2002

By A Customer

I am a grad student who has to read this book every week to do the homework :P. Personally I do not reccommend the book for anyone who doesn't have strong random process background. For average student like me, I found myself read it more than 10 times in some of the topics to get the idea of the section (in order to finish end of chapter's questions). Also, I feel like there are some missing link that the author left out (may be because author assume that you know the background quite well) and that sometimes make the flow of the explanation not smooth.(for me)