Course Description

 

This is a graduate-level course that teaches basics of random process theory with applications to communication theory and systems.  Important topics include analysis of common random processes (e.g. Poisson process, White Noise, Wiener Process, etc.), random sequences, random processes in linear systems, Markov chains, mean-square calculus.

 

The textbook used for the course is, "Probability, Statistics, and Random Processes for Engineers+, 4th Edition, by H. Stark and J. W. Woods.

 

The comprehensive set of videos listed below now cover all the topics in the course; 116 videos with nearly 21 hours of content.

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Video Lectures

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• Course Introduction and Random Variable Review (8 videos, ~58 minutes)

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• Random Vectors: (14 videos, ~164 minutes)

  • Topics include: density and distribution functions, uncorrelated vectors, orthogonal vectors, transformations of random vectors, covariance matrices, eigenvalues/eigenvectors of covariance matrices, covariance diagonalization, Gaussian random vectors.

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• Random Sequences

  • Part 1: (17 videos, ~202 minutes)

    • Topics include: random sequence definition, mean function autocorrelation function, Bernoulli random sequence, arrival time random sequence, random walks, random sequences in discrete-time linear systems

  • Part 2: (11 videos, ~78 minutes)

    • Topics include: Wide-sense stationary (WSS) random sequences, autocorrelation function properties, simplified input/output relationships for WSS random sequences in linear systems, the power spectral density (PSD) function, PSD properties, and PSD examples in Matlab.

  • ​Part 3: (9 videos, ~117 minutes)

    • Topics include: Markov random sequences, Markov chains, state transition matrices, probability row vectors, convergence of sequences, sure convergence, almost sure convergence, and mean-square convergence.​

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• Random Processes

  • Part 1: (10 videos, ~86 minutes)

    • Topics include: Random process definition, mean and autocorrelation functions, asynchronous binary signaling, Poisson random process and properties​

  • Part 1 Cont: (6 videos, ~73 minutes)

    • Topics include: Telegraph random process, PSK random process, Wiener random process (i.e. random walk random process) and properties

  • Part 2: (10 videos, ~106 minutes)

    • Topics include: Markov random processes, Markov chains, state-transition diagrams, random processes in continuous-time linear systems, input/output relationships for mean and autocorrelation functions, white noise random processes

  • Part 3: (8 videos, ~77 minutes)

    • Topics include: Random process properties, simplified input/output relationships for WSS random processes, the power spectral density (PSD) function, PSD properties, and PSD examples.​

  • Part 4: Additional Classification (4 videos, ~35 minutes)

    • Topics include: Wide-sense periodic random processes, cyclostationary random processes, and PSK power spectral density​

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• Mean Square (MS) Calculus

  • Part 1: (13 videos, ~120 minutes)

    • Topics include: Mean-square calculus introduction, mean-square continuous definition and examples, mean-square derivative definition and examples, mean-square integral definition and examples

  • Part 2: (6 videos, ~135 minutes)

    • Topics include: Definitions of mean ergodic, mean-square ergodic, and correlation ergodic random processes; Karhunen-Loeve expansion definition, examples (with Matlab), and proofs.

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Example Problems

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• Random Vectors (5 videos, ~36 minutes)

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Practice Problems

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• Final Exam - Fall 2018

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