本书是一本非常经典的详细介绍检测,估值与调制理论的教学参考书,在美国自1968年首次出版以来,已重印28次.主要包括随机过程的表示,检测与估值的分类,信号检测,信号参数的估计,连续波形的估计,线性估计和线性调制理论等.\r\n
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The area of detection and estimation theory that we shall study in this book represents a combination of the classical techniques of statistical inference and the random process characterization of communication, radar, sonar, and other modern data processing systems. The two major areas of statistical inference are decision theory and estimation theory. In the first case we observe an output that has a random character and decide which of two possible causes produced it. This type of problem was studied in the middle of the eighteenth century by Thomas Bayes [l]. In the estimation theory case the output is related to the value of some parameter of interest, and we try to estimate the value of this parameter. Work in this area was published by Legendre [2] and Gauss [3] in the early nineteenth century.
Significant contributions to the classical theory that we use as background were developed by Fisher [4] and Neyman and Pearson [5] more than 30 years ago. In 1941 and 1942 Kolmogoroff [6] and Wiener [7] applied statistical techniques to the solution of the optimum linear filtering problem. Since that time the application of statistical techniques to the synthesis and analysis of all types of systems has grown rapidly. The application of these techniques and the resulting implications are the subject of this book.
This book and the subsequent volume, Detection, Estimation, and Modulation Theory, Part II, are based on notes prepared for a course entitled " Detection, Estimation, and Modulation Theory," which is taught as a second-level graduate course at M.I.T. My original interest in the material grew out of my research activities in the area of analog modulation theory. A preliminary version of the material that deals with modulation theory was used as a text for a summer course presented at M.I.T. in 1964.
It turned out that our viewpoint on modulation theory could best be understood by an audience with a clear understanding of modern detection and estimation theory. At that time there was no suitable text available to cover the material of interest and emphasize the points that I felt were important, so I started writing notes. It was clear that in order to present the material to graduate students in a reasonable amount of time it would be necessary to develop a unified presentation of the three topics : detection, estimation, and modulation theory, and exploit the fundamental ideas that connected them. As the development proceeded, it grew in size until the material that was originally intended to be background for modulation theory occupies the entire contents of this book. The original material on modulation theory starts at the beginning of the second book. Collectively.
the two books provide a unified coverage of the three topics and their application to many important physical problems.
For the last three years I have presented successively revised versions of the material in my course. The audience consists typically of 40 to 50 students who have completed a graduate course in random processes which covered most of the material in Davenport and Root [8]. In general, they have a good understanding of random process theory and a fair amount of
practice with the routine manipulation required to solve problems. In addition, many of them are interested in doing research in this general area or closely related areas. This interest provides a great deal of motivation which I exploit by requiring them to develop many of the important ideas as problems. It is for this audience that the book is primarily intended. The appendix contains a detailed outline of the course:
On the other hand, many practicing engineers deal with systems that have been or should have been designed and analyzed with the techniques developed in this book. I bave attempted to make the book useful to them.
An earlier version was used successfully as a text for an in-plant course for graduate engineers.
From the standpoint of specific background little advanced material is required. A knowledge of elementary probability theory and second moment characterization of random processes is assumed. Some familiarity with matrix theory and linear algebra is helpful but certainly not necessary.
The level of mathematical rigor is low, although in most sections the results could be rigorously proved by simply being more careful in our derivations.
We have adopted this approach in order not to obscure the important ideas with a lot of detail and to make the material readable for the kind of engineering audience that will find it useful. Fortunately, in almost all cases we can verify that our answers are intuitively logical. It is worthwhile to obseve that this ability to check our answers intuitively would be necessary even if our derivations were rigorous, because our ultimate objective is to obtain an answer that corresponds to some physical system of interest. It is easy to find physical problems in which a plausible mathematical model and correct mathematics lead to an unrealistic answer for the original problem.
We have several idiosyncrasies that it might be appropriate to mention. In general, we look at a problem in a fair amount of detail. Many times we look at the same problem in several different ways in order to gain a better understanding of the meaning of the result. Teaching students a number of ways of doing things helps them to be more flexible in their approach to new problems. A second feature is the necessity for the reader to solve problems to understand the material fully. Throughout the course and the book we emphasize the development of an ability to work problems. At the end of each chapter are problems that range from routine manipulations to significant extensions of the material in the text. In many cases they are equivalent to journal articles currently being published. Only by working a fair number of them is it possible to appreciate the significance and generality of the results. Solutions for an individual problem will be supplied on request, and a book containing solutions to about one third of the problems is available to faculty members teaching the course. We are continually generating new problems in conjunction with the course and will send them to anyone who is using the book as a course text. A third issue is the abundance of block diagrams, outlines, and pictures. The diagrams are included because most engineers (including myself) are more at home with these items than with the corresponding equations.
One problem always encountered is the amount of notation needed to cover the large range of subjects. We have tried to choose the notation in a logical manner and to make it mnemonic. AII the notation is summarized in the glossary at the end of the book. We have tried to make our list of references as complete as possible and to acknowledge any ideas due to other people.
A number of people have contributed in many ways and it is a pleasure to acknowledge them. Professors W. B. Davenport and W. M. Siebert have provided continual encouragement and technical comments on the various chapters. Professors Estil Hoversten and Donald Snyder of the M.I.T.
faculty and Lewis Collins, Arthur Baggeroer, and Michael Austin, three of my doctoral students, have carefully read and criticized the various chapters. Their suggestions have improved the manuscript appreciably. In addition, Baggeroer and Collins contributed a number of the problems in the various chapters and Baggeroer did the programming necessary for many of the graphical results. Lt. David Wright read and criticized Chapter 2. L. A. Frasco and H. D. Goldfein, two of my teaching assistants, worked all of the problems in the book. Dr. Howard Yudkin of Lincoln Laboratory read the entire manuscript and offered a number of important criticisms.
In addition, various graduate students taking the course have made suggestions which have been incorporated. Most of the final draft was typed by Miss Aina Sils. Her patience with the innumerable changes is sincerely appreciated. Several other secretaries, including Mrs. Jarmila
Hrbek, Mrs. Joan Bauer, and Miss Camille Tortorici, typed sections of the various drafts.
As pointed out earlier, the books are an outgrowth of my research interests. This research is a continuing effort, and I shall be glad to send our current work to people working in this area on a regular reciprocal basis.
My early work in modulation theory was supported by Lincoln Laboratory as a summer employee and consultant in groups directed by Dr. Herbert Sherman and Dr. Barney Reiffen. My research at M.I.T. was partly supported by the Joint Services and the National Aeronautics and Space Administration under the auspices of the Research Laboratory of Electronics. This support is gratefully acknowledged.
Harrv L. Van Trees
Cambridge, Massachusetts
October, 1967.
REFERENCES
[l] Thomas Bayes, "An Essay Towards Solving a Problem in the Doctrine of chances," Phil. Trans, 53. 370-418 (l764).
[2] A. M. Legendre,Nouvelles Methodes pour La Ditermination ces Orbites des Cometes, Paris. 1806.
[3] K. F. Gauss, Theory of Motion of Motion of the Heavenly Bodies Moving .About the Sun in
Conic Sections, reprinted by Dover. New York. 1963.
[4] R.A.Fisher, "Theory of StatisticaI Estimation," Proc. Cambridge Philos. Soc., 22,700(1925)
[5] J.Neyman and E. S. Pearson, "On the Problem of the Most Efficient Tests of Statistical Hypotheses," Phil.Trans. Roy. Soc. London, A 231. 289. (1933).
[6] A. kolmogoroff,Interpolation and Extrapolation von Stationaren Zufalligen Folgen," Bull. Acad. Scl. USSR. Ser. Math.5. 1941.
[7] N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Stries. Tech.Press of M.I.T and Wiley, New York, 1949(originally pubished as a classified report in 1942).
[8] W. B.Daevenport and W. L. Root, Random Signals and Nolse. McGraw-Hill. New York, 1958.
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