Random Processes for Engineers

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Cambridge University Press, Mar 12, 2015 - Technology & Engineering
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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).
 

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Contents

Convergence of a sequence of random variables
40
Random vectors and minimum mean squared error estimation
73
Random processes
103
Inference for Markov models
143
Dynamics of countablestate Markov models
167
Basic calculus of random processes
206
Random processes in linear systems and spectral analysis
248
Wiener filtering
280
Martingales
304
Appendix
325
Solutions to even numbered problems
344
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About the author (2015)

Bruce Hajek has been an avid student, instructor, and user of probability theory for his entire career. He is the Mary Lou and Leonard C. Hoeft Chair of Engineering, Center for Advanced Study Professor of Electrical and Computer Engineering, and Professor in the Coordinated Science Laboratory at the University of Illinois. Among his many awards, he is a member of the US National Academy of Engineering and a recipient of the IEEE Koji Kobayashi Computers and Communications Award. He is co-author, with E. Wong, of the more advanced classic book, Stochastic Processes in Engineering Systems, 2nd edition (1985).

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