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Essential background reading for engineers and scientists working in such fields as communications, control, signal, and image processing, radar and sonar, radio astronomy, seismology, remote sensing, and instrumentation.

This book is the result of our teaching over the years an undergraduate course on Linear Optimal Systems to applied mathematicians and a first-year graduate course on Linear Systems to engineers.

This volume is the result of our teaching in the last few years of a first year graduate course on multivariable feedback systems addressed to control engineers. The prerequisites are modest: an undergraduate course in control (for acquaintance with concepts, terms, and design goals) and a senior-graduate course in linear systems.

This book is a revision of Random Point Processes written by D. L. Snyder and published by John Wiley and Sons in 1975. More emphasis is given to point processes on multidimensional spaces, especially to pro- cesses in two dimensions. This reflects the tremendous increase that has taken place in the use of point-process models for the description of data from which images of objects of interest are formed in a wide variety of scientific and engineering disciplines. A new chapter, Translated Poisson Processes, has been added, and several of the chapters of the fIrst edition have been modifIed to accommodate this new material. Some parts of the fIrst edition have been deleted to make room. Chapter 7 of the fIrst edition, which was about general marked point-processes, has been eliminated, but much of the material appears elsewhere in the new text. With some re- luctance, we concluded it necessary to eliminate the topic of hypothesis testing for point-process models. Much of the material of the fIrst edition was motivated by the use of point-process models in applications at the Biomedical Computer Labo- ratory of Washington University, as is evident from the following excerpt from the Preface to the first edition. "e;It was Jerome R. Cox, Jr. , founder and [1974] director of Washington University's Biomedical Computer Laboratory, who ftrst interested me [D. L. S.

This book contains a unified treatment of a class of problems of signal detection theory. This is the detection of signals in addi- tive noise which is not required to have Gaussian probability den- sity functions in its statistical description. For the most part the material developed here can be classified as belonging to the gen- eral body of results of parametric theory. Thus the probability density functions of the observations are assumed to be known, at least to within a finite number of unknown parameters in a known functional form. Of course the focus is on noise which is not Gaussian; results for Gaussian noise in the problems treated here become special cases. The contents also form a bridge between the classical results of signal detection in Gaussian noise and those of nonparametric and robust signal detection, which are not con- sidered in this book. Three canonical problems of signal detection in additive noise are covered here. These allow between them formulation of a range of specific detection problems arising in applications such as radar and sonar, binary signaling, and pattern recognition and classification. The simplest to state and perhaps the most widely studied of all is the problem of detecting a completely known deterministic signal in noise. Also considered here is the detection random non-deterministic signal in noise. Both of these situa- of a tions may arise for observation processes of the low-pass type and also for processes of the band-pass type.

Due to a steady flow of requests over several years, Springer-Verlag now provides a corrected reprint of this text. It is designed to serve as a text for a first semester graduate level course for students in digital communication systems. As a pre- requisite, it is presumed that the reader has an understanding of basic probability and stochastic processes. The treatment of digital communications in this book is intended to serve as an introduction to the subject. Part one is a development of the elements of statistical communication theory and radar detection. The text begins with a general model of a communication system which is extensively developed and the performance analyses of various conventional systems. The first part also serves as introductory material for the second part of the text which is a comprehensive study of the theory of transmitter optimization for coherent and noncoherent digital commu- nication systems, that is, the theory of signal design.

Much of that which is ordinal is modeled as analog. Most computational engines on the other hand are dig- ital. Transforming from analog to digital is straightforward: we simply sample. Regaining the original signal from these samples or assessing the information lost in the sampling process are the fundamental questions addressed by sampling and interpolation theory. This book deals with understanding, generalizing, and extending the cardinal series of Shannon sampling theory. The fundamental form of this series states, remarkably, that a bandlimited signal is uniquely specified by its sufficiently close equally spaced samples. The contents of this book evolved from a set of lecture notes prepared for a graduate survey course on Shannon sampling and interpolation theory. The course was taught at the Department of Electrical Engineering at the University of Washington, Seattle. Each of the seven chapters in this book includes a list of references specific to that chapter. A sequel to this book will contain an extensive bibliography on the subject. The author has also opted to include solutions to selected exercises in the Appendix.

The purpose of this book is to introduce the reader to the basic theory of signal detection and estimation. It is assumed that the reader has a working knowledge of applied probability and random processes such as that taught in a typical first-semester graduate engineering course on these subjects. This material is covered, for example, in the book by Wong (1983) in this series. More advanced concepts in these areas are introduced where needed, primarily in Chapters VI and VII, where continuous-time problems are treated. This book is adapted from a one-semester, second-tier graduate course taught at the University of Illinois and at Princeton University. However, this material can also be used for a shorter or first-tier course by restricting coverage to Chapters I through V, which for the most part can be read with a background of only the basics of applied probability, including random vectors and conditional expectations. Sufficient background for the latter option is given for example in the book by Thomas (1986), also in this series. This treatment is also suitable for use as a text in other modes. For example, two smaller courses, one in signal detection (Chapters II, III, and VI) and one in estimation (Chapters IV, V, and VII), can be taught from the materials as organized here. Similarly, an introductory-level course (Chapters I through IV) followed by a more advanced course (Chapters V through VII) is another possibility.

This book was written as a first treatment of statistical com­ munication theory and communication systems at a senior­ graduate level. The only formal prerequisite is a knowledge of ele­ mentary calculus; however, some familiarity with linear systems and transform theory will be helpful. Chapter 1 is introductory and contains no substantial techni­ cal material. Chapter 2 is an elementary introduction to probability theory at a nonrigorous and non abstract level. It is essential to the remainder of the book but may be skipped (or reviewed has­ tily) by any student who has taken a one-semester undergraduate course in probability. Chapter 3 is a brief treatment of random processes and spec­ tral analysis. It includes an introduction to shot noise (Sections 3.14-3.17) which is not subsequently used explicitly. Chapter 4 considers linear systems with random inputs. It includes a considerable amount of material on narrow-band sys­ tems and on the representation of random processes. Chapter5 treats the matched filter and the linear least mean-squared-error filter at an elementary level but in some detail. Numerous examples are provided throughout the book. Many of these are of an elementary nature and are intended merely to illustrate textual material. A reasonable number of problems of varying difficulty are provided. Instructors who adopt the text for classroom use may obtain a Solutions Manual for most of the problems by writing to the author.