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, 49008-5329
Course/Lecture Overview
•
•
•
•
•
Syllabus
Personal Intro.
Textbook/Materials Used
Additional Reading
ID and Acknowledgment of Policies
• Chapter 1
ECE 3800
2
Syllabus
•
Everything useful for this class can be found on Dr. Bazuin’s web site!
– http://homepages.wmich.edu/~bazuinb/
– http://homepages.wmich.edu/~bazuinb/BJB_CoursesSp15.html
– http://homepages.wmich.edu/~bazuinb/DoorSchSp15.htm
•
The class web site is at
– http://homepages.wmich.edu/~bazuinb/ECE3800/ECE3800_Sp15.html
•
The syllabus …
– http://homepages.wmich.edu/~bazuinb/ECE3800/ECE3800ABET.pdf
– http://homepages.wmich.edu/~bazuinb/ECE3800/Syl_3800.pdf
ECE 3800
3
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, 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, EMU ECE Dept. 2007-
ECE 3800
4
Research and Technical Interests
•
Wireless Communications
–
–
•
Advanced Digital Signal Processing
–
–
•
Xilinx with VHDL coding
Computer arithmetic implementation
Graphic processing units (GPU)
Sunseeker Solar Team Adviser
–
–
–
•
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
–
–
–
•
Physical Layer signal and system implementation
Software Defined Radios (SDR)
Embedded processing systems (TI MSP430 based)
Energy conversion (solar cells, batteries, super capacitors)
Embedded software (control, monitoring, safety, telemetry)
Collaborative Engineering
–
ECE 3800
Supporting other WMU research activities where I can contribute
5
Required Textbook/Materials
• George R. Cooper and Clare D. McGillem, Probabilistic
Methods of Signal and System Analysis, 3rd ed.,Oxford
University Press Inc., 1999.
ISBN: 0-19-512354-9.
•
ECE 3800
The MATH Works,
MATLAB Student Version ($99) or CAE Center
http://www.mathworks.com/
6
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: 013-147122-8.
– 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: 013-231123-2.
•
•
•
Strong candidate for ECE 3800 in Fall 2015.
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 Stochastic
Processes," McGraw-Hill, 1965. ISBM: 07-048448-1.
ECE 3800
7
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 3800
8
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
ECE 3800
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
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, 1999. ISBN: 0-19-512354-9.
9
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
ECE 3800
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
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, 1999. ISBN: 0-19-512354-9.
10
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, 1999. ISBN: 0-19-512354-9.
11
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
ECE 3800
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
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, 1999. ISBN: 0-19-512354-9.
12
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
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
On to the Course
Material
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, 1999. ISBN: 0-19-512354-9.
13