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ECE 537H1S - Random Processes Introduction to the principles and properties of random processes, with applications to communications, control systems, and computer science. Topics include random vectors, random convergence, random processes, specifying random processes, Poisson and Gaussian processes, stationarity, mean square derivatives and integrals, ergodicity, power spectrum, linear systems with stochastic input, mean square estimation, Markov chains, recurrence, absorption, limiting and steady-state distributions, time reversibility, and balance equations. Prerequisites: Introductory probability, linear systems Required textbook: A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, Third Edition, Pearson-Prentice-Hall 2008. Instructor: A. Leon-Garcia (BA 4120; [email protected]) Office hours: Wednesday 1-2 pm Teaching assistant: Amir Tasbihi, [email protected] Lectures: Monday 10-12 pm; Wednesday 11-12pm Bahen 1220, Tutorial: Friday 4-6 pm WB342 Evaluation scheme: Homework, 10%; midterm, 40%; final, 50%. Homework will be graded solely on the basis of effort, not correctness. Solution to the homework problems will be discussed during tutorials. Midterm is scheduled for October 20 during the tutorial period. Undergraduate and graduate students do the same course work but are evaluated on separate scales. # 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 Lecture Tutorial 11-Sep-17 11-Sep-17 13-Sep-17 15-Sep-17 18-Sep-17 18-Sep-17 20-Sep-17 22-Sep-17 25-Sep-17 25-Sep-17 27-Sep-17 29-Sep-17 02-Oct-17 02-Oct-17 04-Oct-17 06-Oct-17 11-Oct-17 13-Oct-17 13-Oct-17 16-Oct-17 16-Oct-17 Midterm 18-Oct-17 20-Oct-17 23-Oct-17 23-Oct-17 25-Oct-17 27-Oct-17 30-Oct-17 30-Oct-17 01-Nov-17 03-Nov-17 06-Nov-17 06-Nov-17 08-Nov-17 10-Nov-17 13-Nov-17 13-Nov-17 15-Nov-17 17-Nov-17 20-Nov-17 20-Nov-17 22-Nov-17 24-Nov-17 27-Nov-17 27-Nov-17 29-Nov-17 01-Dec-17 04-Dec-17 04-Dec-17 06-Dec-17 08-Dec-17 Topic Tutorial Revisiting LLN and CLT Probabilities over Real Line CDF, PDF, PMF Course Introduction; Axioms of Probability, Conditional Probability, Bayes' Rule Total Probability, Independent Events, Bernoulli Trials, Binomial & Poisson Probabilities Random Variables Poisson Process, Stationarity Random Telegraph Process, Shot Noise, Gaussian Process, Wiener Process Tutorial Tutorial Random Processes, Statistics of Random Processes, Multiple Random Processes Vector RVs, Independent RVs, Correlation, Orthogonality, Linear Transformation Gaussian Random Vectors; Conditional Density, Conditional Expectation Convergence of Random Sequence: Sure, Almost Sure, in Probability Convergence of Random Sequence: in Distribution, in Mean Square Sense, Cauchy Criterion IID Processes, Sum Processes Moments and Characteristic Function D-T MC, Chapman-Kolmogorov Equation, Steady State Distributions Irreducibility, Recurrence, Periodicity, Ergodicity Limiting Distributions,Reducible MCs Absorption Probability, Mean Time to Absorption C-T MC, State Sojourn Time, Construction, Transition Densities Transition Densities, Kolmogorov Equations, Limiting and Steady State Distributions LTI Systems LTI Systems, Brownian Motion MS Estimation Linear MS Estimation, Orthogonality Principle Prediction, Interpolation, Smoothing, Wiener Filtering Markov Chains, Motivating Example Continuity, Derivatives, Integrals Fourier Series & Karhunen-Loeve Expansion Review Time, Averages, Ergocity Power Spectral Density, Wiener- Khinchin Theorem Wide-Sense Stationarity, Cyclo-Stationarity Sampling of Bandlimited Processes, Amplitude Modulation Birth-Death Processes, Markovian Queues Time Reversability

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ECE 537H1S - Random Processes

Introduction to the principles and properties of random processes, with applications to communications, control systems, and computer science. Topics include random vectors, random convergence, random processes, specifying random processes, Poisson and Gaussian processes, stationarity, mean square derivatives and integrals, ergodicity, power spectrum, linear systems with stochastic input, mean square estimation, Markov chains, recurrence, absorption, limiting and steady-state distributions, time reversibility, and balance equations.

Prerequisites: Introductory probability, linear systems

Required textbook: A. Leon-Garcia, Probability and Random Processes for Electrical Engineering, Third Edition, Pearson-Prentice-Hall 2008.

Instructor: A. Leon-Garcia (BA 4120; [email protected]) Office hours: Wednesday 1-2 pm

Teaching assistant: Amir Tasbihi, [email protected]

Lectures: Monday 10-12 pm; Wednesday 11-12pm Bahen 1220, Tutorial: Friday 4-6 pm WB342

Evaluation scheme: Homework, 10%; midterm, 40%; final, 50%. Homework will be graded solely on the basis of effort, not correctness. Solution to the homework problems will be discussed during tutorials. Midterm is scheduled for October 20 during the tutorial period. Undergraduate and graduate students do the same course work but are evaluated on separate scales.

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Lecture Tutorial11-Sep-1711-Sep-1713-Sep-17 15-Sep-1718-Sep-1718-Sep-1720-Sep-17 22-Sep-1725-Sep-1725-Sep-1727-Sep-17 29-Sep-1702-Oct-1702-Oct-1704-Oct-17 06-Oct-1711-Oct-1713-Oct-1713-Oct-17 16-Oct-1716-Oct-17 Midterm18-Oct-17 20-Oct-1723-Oct-1723-Oct-1725-Oct-17 27-Oct-1730-Oct-1730-Oct-1701-Nov-17 03-Nov-1706-Nov-1706-Nov-1708-Nov-17 10-Nov-1713-Nov-1713-Nov-1715-Nov-17 17-Nov-1720-Nov-1720-Nov-1722-Nov-17 24-Nov-1727-Nov-1727-Nov-1729-Nov-17 01-Dec-1704-Dec-1704-Dec-1706-Dec-17 08-Dec-17

Topic

Tutorial

RevisitingLLNandCLT

ProbabilitiesoverRealLine

CDF,PDF,PMF

CourseIntroduction;AxiomsofProbability,ConditionalProbability,Bayes'RuleTotalProbability,IndependentEvents,BernoulliTrials,Binomial&PoissonProbabilities

RandomVariables

PoissonProcess,StationarityRandomTelegraphProcess,ShotNoise,GaussianProcess,WienerProcess

TutorialTutorial

RandomProcesses,StatisticsofRandomProcesses,MultipleRandomProcesses

VectorRVs,IndependentRVs,Correlation,Orthogonality,LinearTransformationGaussianRandomVectors;ConditionalDensity,ConditionalExpectationConvergenceofRandomSequence:Sure,AlmostSure,inProbabilityConvergenceofRandomSequence:inDistribution,inMeanSquareSense,CauchyCriterion

IIDProcesses,SumProcesses

MomentsandCharacteristicFunction

D-TMC,Chapman-KolmogorovEquation,SteadyStateDistributionsIrreducibility,Recurrence,Periodicity,ErgodicityLimitingDistributions,ReducibleMCsAbsorptionProbability,MeanTimetoAbsorptionC-TMC,StateSojournTime,Construction,TransitionDensitiesTransitionDensities,KolmogorovEquations,LimitingandSteadyStateDistributions

LTISystemsLTISystems,BrownianMotionMSEstimationLinearMSEstimation,OrthogonalityPrinciplePrediction,Interpolation,Smoothing,WienerFilteringMarkovChains,MotivatingExample

Continuity,Derivatives,Integrals

FourierSeries&Karhunen-LoeveExpansion

Review

Time,Averages,Ergocity

PowerSpectralDensity,Wiener-KhinchinTheorem

Wide-SenseStationarity,Cyclo-Stationarity

SamplingofBandlimitedProcesses,AmplitudeModulation

Birth-DeathProcesses,MarkovianQueuesTimeReversability

Probability, Random Variables and Random Processes - Part 2

AD-A248 730 - DTIC · nonlinear filtering, random fields, point processes and random measures, exchangeable processes, nonstationary processes, Gaussian and non-Gaussian processes,

Basic Random Processes

Random processes. Matlab What is a random process?