Lecture Slides
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EE 603 · Graduate course resource
Random Processes
Lecture Library
A complete, structured path through random variables, random sequences, stochastic processes, and mean-square calculus.
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116lecture videos
~21hours of instruction
12guided collections
4core units
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From probability review
to mean-square calculus.
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Course unit
Foundations
Random variables and vectors
Foundations
Course Introduction & Random Variable Review
Probability spaces, random variables, distributions, moments, Gaussian variables, and joint relationships.
Foundations
Random Vectors
Joint density, uncorrelated and orthogonal vectors, transformations, covariance matrices, eigendecomposition, and Gaussian vectors.
Course unit
Random Sequences
Discrete-time stochastic models
Random Sequences
Random Sequences · Part 1
Definitions, mean and autocorrelation, Bernoulli and arrival-time sequences, random walks, and discrete-time linear systems.
Random Sequences
Random Sequences · Part 2
Wide-sense stationarity, correlation properties, linear systems, power spectral density, and MATLAB examples.
Random Sequences
Random Sequences · Part 3
Markov sequences and chains, transition matrices, probability vectors, and modes of convergence.
Course unit
Random Processes
Continuous-time models and systems
Random Processes
Random Processes · Part 1
Definitions, mean and autocorrelation functions, asynchronous binary signaling, and the Poisson process.
Random Processes
Random Processes · Part 1 Continued
Telegraph, PSK, and Wiener random processes, with important properties and examples.
Random Processes
Random Processes · Part 2
Markov processes, state-transition diagrams, continuous-time linear systems, and white noise.
Random Processes
Random Processes · Part 3
Process properties, WSS input/output relationships, power spectral density, and worked examples.
Random Processes
Random Processes · Part 4
Wide-sense periodic and cyclostationary processes, plus PSK power spectral density.
Course unit
MS Calculus
Continuity, derivatives, integrals, ergodicity
Mean-Square Calculus
Mean-Square Calculus · Part 1
Mean-square continuity, derivatives, integrals, definitions, and examples.
Mean-Square Calculus
Mean-Square Calculus · Part 2
Ergodicity, correlation ergodicity, and the Karhunen–Loève expansion with MATLAB examples and proofs.
Worked examples & supplemental problems
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Course resources
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Exam Archive
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These 18 public lectures provide a strong review of random-variable fundamentals and introduce continuous-time random processes.
▶Lecture 01Random Processes Course Introduction▶Lecture 02Probability Space Definition▶Lecture 03Random Variable Definition▶Lecture 04Distribution and Density Functions▶Lecture 05Mean, Variance, and Moments▶Lecture 06Gaussian Random Variables▶Lecture 07Multiple Random Variable Relationships▶Lecture 082-D Gaussian Random Variables in MATLAB▶Lecture 09Random Process Introduction▶Lecture 10Definitions · Part 1▶Lecture 11Definitions · Part 2▶Lecture 12Mean and Autocorrelation Example▶Lecture 13Asynchronous Binary Signaling · Introduction▶Lecture 14Asynchronous Binary Signaling · Mean▶Lecture 15Asynchronous Binary Signaling · Correlation▶Lecture 16Poisson Process · Introduction▶Lecture 17Poisson Process Properties · Part 1▶Lecture 18Poisson Process Properties · Part 2
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