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Author: Jerry D. Gibson
Publisher: Springer Nature
ISBN: 3031195809
Category : Technology & Engineering
Languages : en
Pages : 161
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Book Description
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 domain sampling theorem. The basics of probability and random processes, including the key concepts of expected value, variance, characteristic functions, common probability distributions, autocorrelation, 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 autocorrelation, power spectral densities, stationarity, and ergodicity
Author: Jerry D. Gibson
Publisher: Springer Nature
ISBN: 3031195809
Category : Technology & Engineering
Languages : en
Pages : 161
Get Book Here
Book Description
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 domain sampling theorem. The basics of probability and random processes, including the key concepts of expected value, variance, characteristic functions, common probability distributions, autocorrelation, 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 autocorrelation, power spectral densities, stationarity, and ergodicity
Author: Venkatarama Krishnan
Publisher: John Wiley & Sons
ISBN: 0471998281
Category : Mathematics
Languages : en
Pages : 739
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Book Description
A resource for probability AND random processes, with hundreds ofworked examples and probability and Fourier transform tables This survival guide in probability and random processes eliminatesthe need to pore through several resources to find a certainformula or table. It offers a compendium of most distributionfunctions used by communication engineers, queuing theoryspecialists, signal processing engineers, biomedical engineers,physicists, and students. Key topics covered include: * Random variables and most of their frequently used discrete andcontinuous probability distribution functions * Moments, transformations, and convergences of randomvariables * Characteristic, generating, and moment-generating functions * Computer generation of random variates * Estimation theory and the associated orthogonalityprinciple * Linear vector spaces and matrix theory with vector and matrixdifferentiation concepts * Vector random variables * Random processes and stationarity concepts * Extensive classification of random processes * Random processes through linear systems and the associated Wienerand Kalman filters * Application of probability in single photon emission tomography(SPECT) More than 400 figures drawn to scale assist readers inunderstanding and applying theory. Many of these figures accompanythe more than 300 examples given to help readers visualize how tosolve the problem at hand. In many instances, worked examples aresolved with more than one approach to illustrate how differentprobability methodologies can work for the same problem. Several probability tables with accuracy up to nine decimal placesare provided in the appendices for quick reference. A specialfeature is the graphical presentation of the commonly occurringFourier transforms, where both time and frequency functions aredrawn to scale. This book is of particular value to undergraduate and graduatestudents in electrical, computer, and civil engineering, as well asstudents in physics and applied mathematics. Engineers, computerscientists, biostatisticians, and researchers in communicationswill also benefit from having a single resource to address mostissues in probability and random processes.
Author: Scott Miller
Publisher: Academic Press
ISBN: 0123870135
Category : Mathematics
Languages : en
Pages : 625
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Book Description
Probability and Random Processes, Second Edition presents pertinent applications to signal processing and communications, two areas of key interest to students and professionals in today's booming communications industry. The book includes unique chapters on narrowband random processes and simulation techniques. It also describes applications in digital communications, information theory, coding theory, image processing, speech analysis, synthesis and recognition, and others. Exceptional exposition and numerous worked out problems make this book extremely readable and accessible. The authors connect the applications discussed in class to the textbook. The new edition contains more real world signal processing and communications applications. It introduces the reader to the basics of probability theory and explores topics ranging from random variables, distributions and density functions to operations on a single random variable. There are also discussions on pairs of random variables; multiple random variables; random sequences and series; random processes in linear systems; Markov processes; and power spectral density. This book is intended for practicing engineers and students in graduate-level courses in the topic. - Exceptional exposition and numerous worked out problems make the book extremely readable and accessible - The authors connect the applications discussed in class to the textbook - The new edition contains more real world signal processing and communications applications - Includes an entire chapter devoted to simulation techniques
Author: William A. Gardner
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 456
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Book Description
Author: Michael B. Pursley
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 176
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Book Description
This book provides an introduction to random processes, and includes content in digital communications and signal processing.Chapter topics cover Probability and Random Variables—Review and Notation, an introduction to Random Processes, Linear Filtering of Random Processes, and Frequency-Domain Analysis of Random Processes in Linear Systems.For practicing engineers.
Author: Steven Kay
Publisher: Springer Science & Business Media
ISBN: 0387241582
Category : Technology & Engineering
Languages : en
Pages : 838
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Book Description
Intuitive Probability and Random Processes using MATLAB® is an introduction to probability and random processes that merges theory with practice. Based on the author’s belief that only "hands-on" experience with the material can promote intuitive understanding, the approach is to motivate the need for theory using MATLAB examples, followed by theory and analysis, and finally descriptions of "real-world" examples to acquaint the reader with a wide variety of applications. The latter is intended to answer the usual question "Why do we have to study this?" Other salient features are: *heavy reliance on computer simulation for illustration and student exercises *the incorporation of MATLAB programs and code segments *discussion of discrete random variables followed by continuous random variables to minimize confusion *summary sections at the beginning of each chapter *in-line equation explanations *warnings on common errors and pitfalls *over 750 problems designed to help the reader assimilate and extend the concepts Intuitive Probability and Random Processes using MATLAB® is intended for undergraduate and first-year graduate students in engineering. The practicing engineer as well as others having the appropriate mathematical background will also benefit from this book. About the Author Steven M. Kay is a Professor of Electrical Engineering at the University of Rhode Island and a leading expert in signal processing. He has received the Education Award "for outstanding contributions in education and in writing scholarly books and texts..." from the IEEE Signal Processing society and has been listed as among the 250 most cited researchers in the world in engineering.
Author: John Bowman Thomas
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 360
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Book Description
Author: Tatsuo Kawata
Publisher: Academic Press
ISBN: 148321852X
Category : Mathematics
Languages : en
Pages : 681
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Book Description
Fourier Analysis in Probability Theory provides useful results from the theories of Fourier series, Fourier transforms, Laplace transforms, and other related studies. This 14-chapter work highlights the clarification of the interactions and analogies among these theories. Chapters 1 to 8 present the elements of classical Fourier analysis, in the context of their applications to probability theory. Chapters 9 to 14 are devoted to basic results from the theory of characteristic functions of probability distributors, the convergence of distribution functions in terms of characteristic functions, and series of independent random variables. This book will be of value to mathematicians, engineers, teachers, and students.
Author: University of Michigan. Engineering Summer Conferences, 1963
Publisher:
ISBN:
Category : Information theory
Languages : en
Pages : 432
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Book Description
Author: Shlomo Engelberg
Publisher: CRC Press
ISBN: 1420007777
Category : Technology & Engineering
Languages : en
Pages : 216
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Book Description
Understanding the nature of random signals and noise is critically important for detecting signals and for reducing and minimizing the effects of noise in applications such as communications and control systems. Outlining a variety of techniques and explaining when and how to use them, Random Signals and Noise: A Mathematical Introduction focuses on applications and practical problem solving rather than probability theory. A Firm Foundation Before launching into the particulars of random signals and noise, the author outlines the elements of probability that are used throughout the book and includes an appendix on the relevant aspects of linear algebra. He offers a careful treatment of Lagrange multipliers and the Fourier transform, as well as the basics of stochastic processes, estimation, matched filtering, the Wiener-Khinchin theorem and its applications, the Schottky and Nyquist formulas, and physical sources of noise. Practical Tools for Modern Problems Along with these traditional topics, the book includes a chapter devoted to spread spectrum techniques. It also demonstrates the use of MATLAB® for solving complicated problems in a short amount of time while still building a sound knowledge of the underlying principles. A self-contained primer for solving real problems, Random Signals and Noise presents a complete set of tools and offers guidance on their effective application.
