John B. Thomas - Böcker

This book was written for an introductory one-term course in probability. It is intended to provide the minimum background in probability that is necessary for students interested in applications to engineering and the sciences. Although it is aimed primarily at upperclassmen and beginning graduate students, the only prere­ quisite is the standard calculus course usually required of under­ graduates in engineering and science. Most beginning students will have some intuitive notions of the meaning of probability based on experiences involving, for example, games of chance. This book develops from these notions a set of precise and ordered concepts comprising the elementary theory of probability. An attempt has been made to state theorems carefully, but the level of the proofs varies greatly from formal arguments to appeals to intuition. The book is in no way intended as a substi­ tu te for a rigorous mathematical treatment of probability. How­ ever, some small amount of the language of formal mathematics is used, so that the student may become better prepared (at least psychologically) either for more formal courses or for study of the literature. 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 all of the problems by writing to the author.

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.

Non-Gaussian Signal Processing is a child of a technological push. It is evident that we are moving from an era of simple signal processing with relatively primitive electronic cir­ cuits to one in which digital processing systems, in a combined hardware-software configura.­ tion, are quite capable of implementing advanced mathematical and statistical procedures. Moreover, as these processing techniques become more sophisticated and powerful, the sharper resolution of the resulting system brings into question the classic distributional assumptions of Gaussianity for both noise and signal processes. This in turn opens the door to a fundamental reexamination of structure and inference methods for non-Gaussian sto­ chastic processes together with the application of such processes as models in the context of filtering, estimation, detection and signal extraction. Based on the premise that such a fun­ damental reexamination was timely, in 1981 the Office of Naval Research initiated a research effort in Non-Gaussian Signal Processing under the Selected Research Opportunities Program.