Probability, Random Variables, and Random Signal Principles

Probability, Random Variables, and Random Signal Principles

Author: Peyton Peebles

Publisher: McGraw-Hill Science/Engineering/Math

Published: 2001

Total Pages: 488

ISBN-13:

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Probability - The Random Variable - Operations on one Random Variable--Expectation - Multiple Random Variables - Operations of Multiple Random Variables - Random Processes-Temporal Characteristics - Random Processes-Spectral Characteristics - Linear Systems with Random Inputs - Optimum Linear Systems - Some Practical Applications of the Theory.


Probability, Random Variables, and Random Signal Principles

Probability, Random Variables, and Random Signal Principles

Author: Peyton Z. Peebles

Publisher: McGraw-Hill Science, Engineering & Mathematics

Published: 1993

Total Pages: 434

ISBN-13:

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Today, any well-designed electrical engineering curriculum must train engineers to account for noise and random signals in systems. The best approach is to emphasize fundamental principles since systems can vary greatly. Professor Peebles's book specifically has this emphasis, offering clear and concise coverage of the theories of probability, random variables, and random signals, including the response of linear networks to random waveforms. By careful organization, the book allows learning to flow naturally from the most elementary to the most advanced subjects. Time domain descriptions of the concepts are first introduced, followed by a thorough description of random signals using frequency domain. Practical applications are not forgotten, and the book includes discussions of practical noises (noise figures and noise temperatures) and an entire special chapter on applications of the theory. Another chapter is devoted to optimum networks when noise is present (matched filters and Wiener filters). This third edition differs from earlier editions mainly in making the book more useful for classroom use. Beside the addition of new topics (Poisson random processes, measurement of power spectra, and computer generation of random variables), the main change involves adding many new end-of-chapter exercises (180 were added for a total of over 800 exercises). The new exercises are all clearly identified for instructors who have used the previous edition.


Introduction to Random Signals and Noise

Introduction to Random Signals and Noise

Author: Wim C. Van Etten

Publisher: John Wiley & Sons

Published: 2006-02-03

Total Pages: 270

ISBN-13: 0470024127

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Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals. Key features: Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains. Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver. Examines optimal filtering methods and their consequences. Presents a detailed discussion of the topic of Poisson processes and shot noise. An excellent resource for professional engineers developing communication systems, semiconductor devices, and audio and video equipment, this book is also ideal for senior undergraduate and graduate students in Electronic and Electrical Engineering.


High-Dimensional Probability

High-Dimensional Probability

Author: Roman Vershynin

Publisher: Cambridge University Press

Published: 2018-09-27

Total Pages: 299

ISBN-13: 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.


Random Processes for Engineers

Random Processes for Engineers

Author: Bruce Hajek

Publisher: Cambridge University Press

Published: 2015-03-12

Total Pages: 429

ISBN-13: 1316241246

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This engaging introduction to random processes provides students with the critical tools needed to design and evaluate engineering systems that must operate reliably in uncertain environments. A brief review of probability theory and real analysis of deterministic functions sets the stage for understanding random processes, whilst the underlying measure theoretic notions are explained in an intuitive, straightforward style. Students will learn to manage the complexity of randomness through the use of simple classes of random processes, statistical means and correlations, asymptotic analysis, sampling, and effective algorithms. Key topics covered include: • Calculus of random processes in linear systems • Kalman and Wiener filtering • Hidden Markov models for statistical inference • The estimation maximization (EM) algorithm • An introduction to martingales and concentration inequalities. Understanding of the key concepts is reinforced through over 100 worked examples and 300 thoroughly tested homework problems (half of which are solved in detail at the end of the book).


Probability, Random Variables, and Random Processes

Probability, Random Variables, and Random Processes

Author: John J. Shynk

Publisher: John Wiley & Sons

Published: 2012-10-15

Total Pages: 850

ISBN-13: 1118393953

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Probability, Random Variables, and Random Processes is a comprehensive textbook on probability theory for engineers that provides a more rigorous mathematical framework than is usually encountered in undergraduate courses. It is intended for first-year graduate students who have some familiarity with probability and random variables, though not necessarily of random processes and systems that operate on random signals. It is also appropriate for advanced undergraduate students who have a strong mathematical background. The book has the following features: Several appendices include related material on integration, important inequalities and identities, frequency-domain transforms, and linear algebra. These topics have been included so that the book is relatively self-contained. One appendix contains an extensive summary of 33 random variables and their properties such as moments, characteristic functions, and entropy. Unlike most books on probability, numerous figures have been included to clarify and expand upon important points. Over 600 illustrations and MATLAB plots have been designed to reinforce the material and illustrate the various characterizations and properties of random quantities. Sufficient statistics are covered in detail, as is their connection to parameter estimation techniques. These include classical Bayesian estimation and several optimality criteria: mean-square error, mean-absolute error, maximum likelihood, method of moments, and least squares. The last four chapters provide an introduction to several topics usually studied in subsequent engineering courses: communication systems and information theory; optimal filtering (Wiener and Kalman); adaptive filtering (FIR and IIR); and antenna beamforming, channel equalization, and direction finding. This material is available electronically at the companion website. Probability, Random Variables, and Random Processes is the only textbook on probability for engineers that includes relevant background material, provides extensive summaries of key results, and extends various statistical techniques to a range of applications in signal processing.


Probability, Random Processes, and Statistical Analysis

Probability, Random Processes, and Statistical Analysis

Author: Hisashi Kobayashi

Publisher: Cambridge University Press

Published: 2011-12-15

Total Pages: 813

ISBN-13: 1139502611

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Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals.