Download EE385 Random Signals and Noise Summer 2016

EE385 Random Signals and Noise
Summer 2016
Instructor
John Stensby, EB 217I, Office Hours: Mon., Wed. 2:45 – 4:45 PM, or by Appointment.
[email protected]
Course Material
1. G. Cooper, C. McGillem, Probabilistic Methods of Signal and System Analysis
2. The most recent version of the class notes can be printed from the EE385 home page
http://www.ece.uah.edu/courses/ee385/
Course Outline/Goal/Recommendation
The course material will come from the first eight chapters of the above-mentioned class notes. Most of this
material is contained in the first eight chapters of the required text. This material satisfies the course goal of
providing the student with a background in applied probability, statistics and random processes that is necessary
to undertake courses in communication theory, radar, signal processing and similar areas. The Schaum’s
outline by Hsu (reference #1 below) is highly recommended. This reference covers most of the course, and it
provides many worked example problems. This semester, your smartest move would be to get and study Hsu’s
outline.
Grading
Midterm
Weekly Short Tests
Final Exam
30%
35%
35%
Notes
1. Weekly homework assignments will be made. Solutions will be provided as .pdf files that are e-mailed to
each student, usually within one week of the assignment. Weekly assigned homework will not be graded.
2. Please use on line Banner to update/check your UAH e-mail address. Regularly check your UAH e-mail inbox.
3. The closed-book short tests will come from the homework and/or example problems worked in class. I will
supply one problem – which is very similar to a homework problem or problem worked in class – and allow 1015 minutes for its completion. Expect one every week. I will drop the lowest short-test grade (to compensate
for absences – makeups of short quizzes will not be given).
4. The midterm and final will be closed book since they will be homework-based, or they will come from the
problems that I worked on the board. That is, the majority of midterm/final problems will be modified
homework problems and problems worked in class.
5. The University of Alabama in Huntsville will make reasonable accommodations for students with
documented disabilities. If you need support or assistance because of a disability, you may be eligible for
academic accommodations. Students should identify themselves to the Disability Support Services Office
(256.824.6203 or 136 Madison Hall) and their instructor as soon as possible to coordinate accommodations. A
Disability Accommodation statement is placed on course syllabi to indicate the university's willingness to
provide reasonable accommodations to a student with a disability, as required by federal law.
References
1. H. Hsu, Probability, Random Variables, and Random Processes, McGraw Hill, 1997 (Schaum’s
Series)
2. A. Papoulis, Probability, Random Variables and Stochastic Processes, Third Edition, McGraw-Hill,
York, 1991.
3. H Stark, J. Woods, Probability, Random Processes, and Estimation Theory for Engineers,
Edition, Prentice Hall, 1994.
Second
Outline
New
4. P. Peebles, Probability, Random Variables and Random Signals Principles, McGraw Hill, 1980.
5. G.R. Grimmett, D.R. Stirzaker, Probability and Random Processes, Oxford Science Publications,1992.
6. Google, Online Searches Often Produce Good Results
Chapter 1: Introduction to Probability
1) The Classical Approach to Probability
2) The Relative Frequency Approach to Probability
3) The Axiomatic Approach to Probability
4) Elementary Set Theory
5) Probability Space: Sample Space, -Algebra and Probability Measure
6) Conditional Probability
7) Theorem of Total Probability - Discrete Form
8) Bayes Theorem
9) Independence of Events
10) Cartesian Product of Sets
11) Independent Bernoulli Trials
12) Gaussian Function
13) DeMoivre-Laplace Theorem
14) Law of Large Numbers
15) Poisson Theorem and Random Points
Chapter 2: Random Variables
1) Random Variables
2) Distribution and Density Function
3) Continuous/Discrete/Mixed Random Variables
4) Normal/Gaussian Random Variable
5) Uniform Random Variable
6) Binomial Random Variable
7) Poisson Random Variable
8) Rayleigh Random Variable
9) Exponential Random Variable
10) Conditional Distribution/Density
11) Theorem of Total Probability - Continuous Form
12) Bayes Theorem - Continuous Form
13) Maximum A-Posteriori Estimate
14) Expectation
15) Variance and Standard Deviation
16) Moments
17) Conditional Expectation
18) Tchebycheff Inequality
19) Poisson Points Applied to System Reliability
Chapter 3: Multiple Random Variables
1) Joint Distribution/Density
2) Jointly Gaussian Random Variables
3) Independence of Random Variables
4) Expectation of a Product of Random Variables
5) Variance of a Sum of Independent Random Variables
6) Random Vectors and Covariance Matrices
Chapter 4: Function of Random Variables
1) Transformation of One Random Variable Into Another
2) Determination of Distribution/Density of Transformed Random Variables
3) Expected Value of Transform Random Variable
4) Characteristic Functions and Applications
5) Characteristic Function for Gaussian Random Vectors
6) Moment Generating Function
7) One Function of Two Random Variables
8) Leibnitz’s Rule
9) Two Functions of Two Random Variables
10) Joint Density Functions
11) Linear Transformation of Gaussian Random Variables
Chapter 5: Moments and Conditional Statistics
1) Expected Value of a Function of Two Random Variables
2) Covariance
3) Correlation Coefficient
4) Uncorrelated and Orthogonal Random Variables
5) Joint Moments
6) Conditional Distribution/Density: One Random Variable Conditioned on Another
7) Conditional Expectation
8) Application of Conditional Expectation: Bayesian Estimation
9) Conditional Multi-dimensional Gaussian Density
Chapter 6: Random Processes
1) Definitions and Examples of Random Processes
2) Continuous and Discrete Random Processes
3) Distribution and Density Functions
4) Stationary Random Processes
5) First- and Second-Order Probabilistic Averages
6) Wide-Sense Stationary Processes
7) Ergodic Processes
8) Classical Random Walk
9) Wiener Process As a Limit of the Random Walk
10) Independent Increments
11) Diffusion Equation for Transition Density
12) Probability Current
13) Solution of Diffusion Equation by Transform Techniques
Chapter 7: Correlation Functions
1) Autocorrelation Function
2) Autocovariance Function
3) Correlation Function
4) Properties of Autocorrelation Function for Real-Valued WSS Random Processes
5) Random Binary Waveform
6) Poisson Random Points (Revisited)
7) Poisson Random Processes
8) Autocorrelation of Poisson Processes
9) Semi-Random Telegraph Signal
10) Random Telegraph Signal
11) Autocorrelation of Wiener Process
12) Correlation Time
13) Crosscorrelation Function
14) Input/Output Cross Correlation for Linear Systems
15) Autocorrelation of System Output in Terms of Autocorrelation of Input
Chapter 8: Power Density Spectrum
Definition of Power spectrum of a Stationary Process
Calculation of Power spectrum of a Process
Rational Power Spectrums
Wiener-Khinchine theorem
Application to Random Telegraph Signal
Power Spectrum of System Output in Terms of Power Spectrum of System Input
Noise Equivalent Bandwidth of a Lowpass System or Filter
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