Fourier Transforms, Filtering, Probability and Random Processes: Introduction to Communication Systems

by Jerry D. Gibson

Overview

This book provides the background and the mathematical methods necessary to understand the basic transforms in signal processing and linear systems and probability and random processes to prepare for in depth study of analog and digital communications systems.

This tutorial presentation provides developments of Fourier series and other orthogonal series, including trigonometric and complex exponential Fourier series, least squares approximations and generalized Fourier series, and the spectral content of periodic signals.

This text thoroughly covers Fourier transform pairs for continuous time signals, Fourier transform properties, and the magnitude and phase of Fourier transforms.

The author includes discussions of techniques for the analysis of continuous time linear systems in the time and frequency domains with particular emphasis on the system transfer function, impulse response, system/filter bandwidth, power and energy calculations, and the time domainsampling theorem.

The basics of probability and random processes, including the key concepts of expected value, variance, characteristic functions, common probability distributions, auorrelation, power spectral densities, wide sense stationarity, and ergodicity, are all developed in some detail. Many examples and problems are included to illustrate and examine these topics.

• Provides developments of Fourier series and other orthogonal series

• Presents fundamental Fourier transform properties and example applications

• Discusses techniques for the analysis of continuous time linear systems in the time and frequency domains

• Presents a fundamental development of probability and random variables

• Develops the basic ideas of random processes including auorrelation, power spectral densities, stationarity, and ergodicity

Product Details

ISBN-13:	9783031195792
Publisher:	Springer International Publishing
Publication date:	03/06/2023
Series:	Synthesis Lectures on Communications
Edition description:	2023
Pages:	156
Product dimensions:	6.61(w) x 9.45(h) x (d)

About the Author

Jerry D. Gibson is Professor of Electrical and Computer Engineering at the University of California, Santa Barbara. He is co-author of the books Digital Compression for Multimedia (Morgan-Kaufmann, 1998) and Introduction to Nonparametric Detection with Applications (Academic Press, 1975 and IEEE Press, 1995) and author of the textbook, Principles of Digital and Analog Communications (Prentice-Hall, second ed., 1993). He is Editor-in-Chief of The Mobile Communications Handbook (CRC Press, 3rd ed., 2012), Editor-in-Chief of The Communications Handbook (CRC Press, 2nd ed., 2002), and Editor of the book, Multimedia Communications: Directions and Innovations (Academic Press, 2000). His most recent books are Rate Distortion Bounds for Voice and Video (Coauthor with Jing Hu, NOW Publishers, 2014), and Information Theory and Rate Distortion Theory for Communications and Compression (Morgan-Claypool, 2014).

Dr. Gibson was Associate Editor for Speech Processing for the IEEE Transactions on Communications from 1981 to 1985 and Associate Editor for Communications for the IEEE Transactions on Information Theory from 1988-1991. He was an IEEE Communications Society Distinguished Lecturer for 2007-2008.

In 1990, Dr. Gibson received The Fredrick Emmons Terman Award from the American Society for Engineering Education, and in 1992, he was elected Fellow of the IEEE. He was the recipient of the 1993 IEEE Signal Processing Society Senior Paper Award for the Speech Processing area. He received the IEEE Transactions on Multimedia Best Paper Award in 2010 and the IEEE Technical Committee on Wireless Communications Recognition Award for contributions in the area of Wireless Communications Systems and Networks in 2009.

Table of Contents

Preface.- Orthogonal Functions an Fourier Series.- Fourier Transforms.- Linear Systems.- Convolution and Filtering.