ECE 3800 Probabilistic Methods of Signal and System Analysis

Transcription

1 ECE 3800 Probabilistic Methods of Signal and System Analysis Dr. Bradley J. Bazuin Western Michigan University College of Engineering and Applied Sciences Department of Electrical and Computer Engineering 1903 W. Michigan Ave. Kalamazoo MI,

2 Course/Lecture Overview Syllabus Personal Intro. Textbook/Materials Used Additional Reading ID and Acknowledgment of Policies Chapter 1 ECE

3 Syllabus Everything useful for this class can be found on Dr. Bazuin s web site! The class web site is at The syllabus ECE

4 Dr. Bradley J. Bazuin Born and raised in Grand Rapids, Michigan Education Undergraduate BS in Engineering and Applied Sciences, Extensive Electrical Engineering from Yale University in 1980 Graduate MS and PhD in Electrical Engineering from Stanford University in 1982 and 1989, respectively. Industrial Employment Part-time ARGOSystems, Inc., Sunnyvale, CA, Full-time ARGOSystems, Inc., Sunnyvale, CA, Full-time Radix Technologies, Mountain View, CA, Academics Term-appointed Faculty, WMU ECE Dept Tenure track Assistant Professor, WMU ECE Dept Tenured Associate Professor, EMU ECE Dept ECE

5 Research and Technical Interests Wireless Communications Physical Layer signal and system implementation Software Defined Radios (SDR) Advanced Digital Signal Processing Algorithmic techniques for processing detecting, estimating and exploiting signals (communications, electronics, and sensors). Multirate signal processing, estimation theory, adaptive signal processing Computer Architectures for signal processing Xilinx with VHDL coding Computer arithmetic implementation Graphic processing units (GPU) Sunseeker Solar Team Adviser Embedded processing systems (TI MSP430 based) Energy conversion (solar cells, batteries, super capacitors) Embedded software (control, monitoring, safety, telemetry) Collaborative Engineering Supporting other WMU research activities where I can contribute ECE

6 Required Textbook/Materials George R. Cooper and Clare D. McGillem, Probabilistic Methods of Signal and System Analysis, 3rd ed.,oxford University Press Inc., ISBN: The MATH Works, MATLAB Student Version ($99) or CAE Center ECE

7 Other Books and Materials Alberto Leon-Garcia, Probability, Statistics, and Random Processes For Electrical Engineering, 3rd ed., Pearson Prentice Hall, Upper Saddle River, NJ, 2008, ISBN: Graduate text used for ECE 5820 H. Stark and J.W. Woods, Probability, Statistics and Random Processes dor Engineers, 4th ed.," Prentice-Hall, Inc., Upper Saddle River, NJ, 2012, ISBN: Strong candidate for ECE 3800 in Fall Schaum's Outline of Probability and Statistics, 2nd Edition, M.R. Spiegel, Deceased, J.J. Schiller, R.A. Srinivasan, McGraw-Hill, ISBN: A. Papoulis, "Probability, Random Variables, and Stochastic Processes," McGraw-Hill, ISBM: ECE

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

9 Course/Text Overview 1. Introduction to Probability Random Experiments and Events Definitions of Probability Probabilistic Experiments Compound Events Conditional Probability Bayes Theorem Digital Communications Systems Random Variables Bernoulli Trials Reliability Simulating Probabilistic Experiments 2. Random Variables Concept of a Random Variable Distribution Functions Density Functions Mean Values and Statistical Moments Uniform Distribution Gaussian Distribution Exponential Distributions Other Probability Density Functions and Distributions Conditional Probability Distribution and Density Functions Exam #1 ECE 3800 Based on materials in the course textbook: Probabilistic Methods of Signal and System Analysis (3rd ed.) by George R. Cooper and Clare D. McGillem; Oxford Press, ISBN:

10 Course/Text Overview (2) 3. Several Random Variables Two Dimensional Random Variables Probability in Two Dimensions, Conditional Probability-- Revisited Statistical Independence Two Dimensional Statistics, Correlation between Random Variables Density Function of the Linear Combination of Two Random Variables Multi-input Electrical Circuits Simulating Convolution Integrals 4. Elements of Statistics The Sampling Problem Unbiased Estimators Sampling Theory--The Sample Mean and Variance Sampling Theorem Sampling Distributions and Confidence Intervals Student s T-Distribution Hypothesis Testing Curve Fitting and Linear Regression Correlation Between Two Sets of Data 5. Random Processes Continuous and Discrete Random Processes Classification of Random Processes Deterministic and Nondeterministic Random Processes Stationary and Nonstationary Random Processes Stationarity Time Averages and Statistical Mean Ergodic and Nonergodic Random Processes Ergodicity Measurement of Process Parameters Smoothing Data with a Moving Window Average Simulating a Random Process Exam #2 ECE 3800 Based on materials in the course textbook: Probabilistic Methods of Signal and System Analysis (3rd ed.) by George R. Cooper and Clare D. McGillem; Oxford Press, ISBN:

11 Course/Text Overview (3) 6. Correlation Functions Autocorrelation of a Binary/Bipolar Process of a Sinusoidal Process Linear Transformations Properties of Autocorrelation Functions Measurement of Autocorrelation Functions An Anthology of Signals Crosscorrelation Functions Properties of Crosscorrelation Functions Examples and Applications of Crosscorrelation Functions Correlation Matrices For Sampled Functions 7. Spectral Density Relation of Spectral Density to the Fourier Transform Weiner-Khinchine Relationship Properties of Spectral Density Spectral Density and the Complex Frequency Plane Mean-Square Values From Spectral Density Relation of Spectral Density to the Autocorrelation Function White Noise, Black Noise, Pink Noise Contour Integration (Appendix I) Cross-Spectral Density Autocorrelation Function Estimate of Spectral Density Periodogram Estimate of Spectral Density Exam #3 ECE 3800 Based on materials in the course textbook: Probabilistic Methods of Signal and System Analysis (3rd ed.) by George R. Cooper and Clare D. McGillem; Oxford Press, ISBN:

12 Course/Text Overview (4) 8. Response of Linear Systems to Random Inputs Linear Systems Analysis in the Time Domain Mean and Variance Value of System Output Autocorrelation Function of System Output Crosscorrelation between Input and Output Example of Time-Domain System Analysis Analysis in the Frequency Domain Spectral Density at the System Output Frequency Limited Filtering Bandlimited White Noise SIMO Systems Cross-Spectral Densities between Input and Output Examples of Frequency-Domain Analysis Numerical Computation of System Output Simulating Stochastic System Responses 9. Optimum Linear Systems System Performance Criteria Criteria of Optimality Restrictions on the Optimum System Optimization by Parameter Adjustment (Variation of Parameters) Matched Filtering Systems That Maximize Signal-to-Noise Ratio Systems That Minimize Mean-Square Error Weiner Filters Final Exam ECE 3800 Based on materials in the course textbook: Probabilistic Methods of Signal and System Analysis (3rd ed.) by George R. Cooper and Clare D. McGillem; Oxford Press, ISBN:

13 Chapter 1: Introduction to Probability Section Headings Engineering Applications of Probability Random Experiments and Events Definitions of Probability The Relative Frequency Approach Elementary Set Theory The Axiomatic Approach Conditional Probability Independence Combined Experiments Bernoulli Trials Applications of Bernoulli Trials On to the Course Material Concepts and Applications Random Experiments and Events Definitions of Probability Probabilistic Experiments Compound Events Conditional Probability Bayes Theorem Digital Communications Systems Random Variables Bernoulli Trials Reliability Simulating Probabilistic Experiments ECE 3800 Based on materials in the course textbook: Probabilistic Methods of Signal and System Analysis (3rd ed.) by George R. Cooper and Clare D. McGillem; Oxford Press, ISBN: