ECE 3800 Probabilistic Methods Of Signal And System Analysis

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ECE 3800Probabilistic Methods of Signaland System AnalysisDr. Bradley J. BazuinWestern Michigan UniversityCollege of Engineering and Applied SciencesDepartment of Electrical and Computer Engineering1903 W. Michigan Ave.Kalamazoo MI, 49008-5329

Course/Lecture Overview SyllabusPersonal Intro.Textbook/Materials UsedAdditional ReadingID and Acknowledgment of Policies Chapter 1ECE 38002

Syllabus Everything useful for this class can be found on Dr. Bazuin’s web site!– http://homepages.wmich.edu/ bazuinb/ The class web site is at– https://homepages.wmich.edu/ bazuinb/ECE3800/ECE3800 Fa16.html The syllabus – http://homepages.wmich.edu/ bazuinb/ECE3800/ECE3800ABET.pdf– http://homepages.wmich.edu/ bazuinb/ECE3800/Syl 3800.pdfECE 38003

Dr. Bradley J. Bazuin Born and raised in Michigan, Grand Rapids – Forest Hills NorthernEducation– Undergraduate BS in Engineering and Applied Sciences, ExtensiveElectrical Engineering from Yale University in 1980– Graduate MS and PhD in Electrical Engineering from Stanford Universityin 1982 and 1989, respectively. Industrial Employment– Part-time ARGOSystems, Inc., Sunnyvale, CA, 1981-1989– Full-time ARGOSystems, Inc., Sunnyvale, CA, 1989-1991– Full-time Radix Technologies, Mountain View, CA, 1991-2000 Academics– Term-appointed Faculty, WMU ECE Dept. 2000-2001– Tenure track Assistant Professor, WMU ECE Dept. 2001-2007– Tenured Associate Professor, WMU ECE Dept. 2007-ECE 38004

Research and Technical Interests Wireless Communications––– Advanced Digital Signal Processing–– Center for the Advancement of Printed ElectronicsCenter for Advanced Smart Sensors and StructuresSunseeker Solar Team Adviser & WMU Educational Solar Garden Technical Director––– Algorithmic techniques for processing detecting, estimating and exploiting signals(communications, electronics, and sensors).Multirate signal processing, estimation theory, adaptive signal processingCAPE & CASSS–– Physical Layer signal and system implementationSoftware Defined Radios (SDR) - USRP & GNU radioXilinx with VHDL coding and Graphic processing units (GPU)Embedded processing systems (TI MSP430 based)Embedded software (control, monitoring, safety, telemetry)Energy conversion (solar cells, batteries, super capacitors)Collaborative Engineering–ECE 3800Supporting other WMU research activities where I can contribute5

Required Textbook/Materials Henry Stark and John W. Woods, Probability, Statistics,and Random Variables for Engineers, 4th ed., PearsonEducation Inc., 2012. ISBN: 978-0-13-231123-6. The MATH Works,MATLAB Student Version ( 99) or CAE Centerhttp://www.mathworks.com/–Learn MATLAB for free ECE .html6

Other Books and Materials George R. Cooper and Clare D. McGillem, Probabilistic Methods ofSignal and System Analysis, 3rd ed., Oxford University Press Inc.,1999. ISBN: 0-19-512354-9.– Previous text used for ECE 3800 Alberto Leon-Garcia, “Probability, Statistics, and Random ProcessesFor Electrical Engineering, 3rd ed.”, Pearson Prentice Hall, UpperSaddle River, NJ, 2008, ISBN: 013-147122-8.– Graduate text used for ECE 5820 Schaum's Outline of Probability and Statistics, 2nd Edition, M.R.Spiegel, Deceased, J.J. Schiller, R.A. Srinivasan, McGraw-Hill, 2000.ISBN: 0071350047.A. Papoulis, "Probability, Random Variables, and StochasticProcesses," McGraw-Hill, 1965. ISBM: 07-048448-1.ECE 38007

Identification and Acknowledgement Identification for Grade Posting,Acknowledgment of completing prerequisites,Reminder of Course and University Policies, andAcknowledgement and Signature Block Please read, provide unique identification, sign and date,and return to Dr. Bazuin.ECE 38008

Course/Text Overview1 Introduction to oduction: Why Study Probability?The Different Kinds of ProbabilityMisuses, Miscalculations, and Paradoxes inProbabilitySets, Fields, and EventsAxiomatic Definition of ProbabilityJoint, Conditional, and Total Probabilities;IndependenceBayes’ Theorem and ApplicationsCombinatoricsBernoulli Trials–Binomial and MultinomialProbability LawsAsymptotic Behavior of the Binomial Law: ThePoisson LawNormal Approximation to the Binomial Law2 Random on of a Random VariableCumulative Distribution FunctionProbability Density Function (pdf)Continuous, Discrete, and Mixed Random VariablesConditional and Joint Distributions and DensitiesFailure Rates3 Functions of Random Variables3.13.23.33.43.5IntroductionSolving Problems of the Type Y g(X)Solving Problems of the Type Z g(X, Y )Solving Problems of the Type V g(X, Y ),W h(X, Y )Additional ExamplesExam #1ECE 3800Based on materials in the course textbook: Henry Stark and John W. Woods, Probability, Statistics, andRandom Variables for Engineers, 4th ed., Pearson Education Inc., 2012. ISBN: 978-0-13-231123-6.9

Course/Text Overview (2)4. Expectation and Moments4.14.24.34.44.54.64.74.8Expected Value of a Random VariableConditional ExpectationsMoments of Random VariablesChebyshev and Schwarz InequalitiesMoment-Generating FunctionsChernoff BoundCharacteristic FunctionsAdditional Examples5 Random Vectors (Highlights Only)5.15.25.35.45.55.65.7Joint Distribution and DensitiesMultiple Transformation of Random VariablesOrdered Random VariablesExpectation Vectors and Covariance MatricesProperties of Covariance MatricesThe Multidimensional Gaussian (Normal) LawCharacteristic Functions of Random Vectors6 Statistics: Part 1 Parameter Estimation6.1 Estimation of the MeanEstimation of the Variance and CovarianceSimultaneous Estimation of Mean and VarianceEstimation of Non-Gaussian Parameters from LargeSamplesMaximum Likelihood EstimatorsOrdering, more on Percentiles, Parametric VersusNonparametric StatisticsEstimation of Vector Means and Covariance MatricesLinear Estimation of Vector Parameters7 Statistics: Part 2 Hypothesis Testing7.1 Bayesian Decision Theory7.27.37.47.5Likelihood Ratio TestComposite HypothesesGoodness of FitOrdering, Percentiles, and RankExam #2ECE 3800Based on materials in the course textbook: Henry Stark and John W. Woods, Probability, Statistics, andRandom Variables for Engineers, 4th ed., Pearson Education Inc., 2012. ISBN: 978-0-13-231123-6.10

Course/Text Overview (3)8 Random Sequences8.18.28.38.48.58.68.78.8Basic ConceptsBasic Principles of Discrete-Time Linear SystemsRandom Sequences and Linear SystemsWSS Random SequencesPower Spectral DensityInterpretation of the psdMarkov Random SequencesARMA ModelsMarkov ChainsVector Random Sequences and State EquationsConvergence of Random SequencesLaws of Large Numbers9 Random Processes9.1 Basic Definitions9.2 Some Important Random Processes9.3 Continuous-Time Linear Systems with Random InputsWhite Noise9.4 Some Useful Classifications of Random ProcessesStationarity9.5 Wide-Sense Stationary Processes and LSI SystemsPower Spectral DensityAn Interpretation of the psdMore on White Noise9.6 Periodic and Cyclostationary Processes9.7 Vector Processes and State EquationsExam #3ECE 3800Based on materials in the course textbook: Henry Stark and John W. Woods, Probability, Statistics, andRandom Variables for Engineers, 4th ed., Pearson Education Inc., 2012. ISBN: 978-0-13-231123-6.11

Course/Text Overview (4)10 Advanced Topics in Random Processes10.110.210.310.410.510.6Mean-Square (m.s.) CalculusMean-Square Stochastic IntegralsMean-Square Stochastic Differential EquationsErgodicity [10-3]Karhunen—Lo eve ExpansionRepresentation of Bandlimited and Periodic Processes11 Applications to Statistical SignalProcessing11.1 Estimation of Random Variables and Vectors11.2 Innovation Sequences and Kalman FilteringKalman Predictor and FilterError-Covariance Equations11.3 Wiener Filters for Random SequencesCausal Wiener Filter11.4 Expectation-Maximization AlgorithmLog-likelihood for the Linear TransformationLog-likelihood Function of Complete Data11.5 Hidden Markov Models (HMM)Viterbi Algorithm and the Most Likely State Sequencefor the Observations11.6 Spectral EstimationThe Periodogram11.7 Simulated AnnealingFinal ExamECE 3800Based on materials in the course textbook: Henry Stark and John W. Woods, Probability, Statistics, andRandom Variables for Engineers, 4th ed., Pearson Education Inc., 2012. ISBN: 978-0-13-231123-6.12

Chapter 1: Introduction to Probability Section ion: Why Study Probability?The Different Kinds of ProbabilityMisuses, Miscalculations, and Paradoxes in ProbabilitySets, Fields, and EventsAxiomatic Definition of ProbabilityJoint, Conditional, and Total Probabilities; IndependenceBayes’ Theorem and ApplicationsCombinatoricsBernoulli Trials–Binomial and Multinomial Probability LawsAsymptotic Behavior of the Binomial Law: The Poisson LawNormal Approximation to the Binomial LawOn to the CourseMaterialECE 3800Based on materials in the course textbook: Henry Stark and John W. Woods, Probability, Statistics, andRandom Variables for Engineers, 4th ed., Pearson Education Inc., 2012. ISBN: 978-0-13-231123-6.13

Advanced Digital Signal Processing . techniques for processing detecting, estimating and exploiting signals (communications, electronics, and sensors). – Multirate signal processing, estimation theory, adaptive signal processing . 1965. ISBM: 07-048448-1. ECE 3800 7. ECE 3800 8 Id

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