THE UNIVERSITY OF THE WEST INDIES ST. AUGUSTINE, TRINIDAD AND TOBAGO, WEST INDIES FACULTY OF ENGINEERING Department of Electrical and Computer Engineering MASc. Electrical and Computer Engineering
ECNG 6700 Stochastic Processes http://ibrir.free.fr / Semester I; 2012 / 2013
1
GENERAL INFORMATION
Course level: Course status:
Level M √ Core Elective Occasional
Semester(s) offered: Delivery mode:
Credits:
3
Estimated total study hours1:
Estimated enrollment:
To be defined
Course Dependencies2
Pre-Requisites – Basic notions of Probabilities, and systems. Other – None.
Recommended prior knowledge skills3:
I √ Lecture √ Online Lab Other 3hrs (weekly) 39hrs (semester)
Upon entering this course, all the students should be able to: Demonstrate understanding of the fundamental theory of signals and systems; Be able to perform numerical simulations using Matlab/Simulink software; Apply basic results obtained in elementary courses as probability, statistics, and signal processing courses including Fourier analysis, z-transform, and Laplace transform.
1More information on UWI regulations and policies can be found on the web site of the course.
Course Staff
Dr. Salim Ibrir
2 2.1
Position/Role
Senior Lecturer
E-mail
[email protected]
Office Phone Ext Rm 320 83147
Office Hours 9 am2pm
COURSE OVERVIEW Course Description
This course gives an introduction to the notion and applications of the stochastic processes that may appear in many fields of engineering including communications, signal processing, digital systems, and control. The course materials include both continuous and discrete random processes, correlation and power spectral density, Kalman and Weiner optimal filtering, Markov chains, and decision theory. 2.2
Course Rationale
An exposure to such a course, enable the students to identify, analyze, and model a standard stochastic process that may appear in practice. A major concern of this course is to put more light on the analysis and identification of stochastic processes that are encountered in many fields of engineering including, but not limited to signal processing, statistics, and control systems. This course is considered as a core course in the postgraduate programme leading to a Master of Applied Science (MASc) in Electrical & Computer Engineering with majors in Control Systems.
2.3
Course Aims
The aims of the stochastic processes course are given in the following items: Analysis of the behaviors of dynamical systems whose inputs and outputs are contaminated by random noise; Design of filters and controllers for stochastic systems; Design of optimal and Kalman filters in continuous time and discrete time; Decision making under noisy environments.
2.4
Course Learning Outcomes
The 4 (four) course-learning outcomes are summarized in the following Table.
Upon successful completion of ECNG 6700, attendees will be able to: 1. Recall the notions of probabilities and Statistics. Define and classify continuous time, discrete time, and multiple random variables. Introduce, characterize, and define the concept of stochastic processes in connection with the study of fluctuations and noise in physical systems. Define the notions of Markov chains, Poisson processes, and Weiner processes. 2. Analysis and processing of random processes. Define the notions of continuity, differentiation, integration, power spectral densities, and white noise. Synthesis of the responses of linear systems to random inputs using Matlab/Simulink environment software. 3. Design, assess, simulate, and synthesize optimal filters including Maximum-Likelihood estimators, Bayes’ estimators, and MeanSquare estimators. Demonstrate the effectiveness of the design by numerical simulations using (Matlab/Simulink). Design of autoregressive models using Matlab/Simulink. 4. Analyze and discuss decision methods with and introduction to elementary queuing theory.
Cognitive Level Knowledge and comprehension
Analysis, Knowledge, synthesis, and application Synthesis, evaluation and application
Analysis and comprehension
3 3.1
COURSE ASSESSMENT Breakdown of Assessment Artifacts and Linkage to Course Learning Outcomes
The details of the learning outcomes are given in section 2.4 and they are classified into four independent Los.
Assessment Artifact
Course LOs Covered LO1 LO2 LO3 LO4
Required to
Weight %
Details (e.g. type - written, oral, practical; duration) Course work is given as series of problems and simulation exercises that are partially solved. Written exam of 3 hours. Closed-book exam. See UWI regulations at the end of this outline.
pass course
Course Work
⊗
⊗
⊗
⊗
NO
0
Final Exam
⊗
⊗
⊗
⊗
YES
100
TOTAL1 Key 1 Distribution of LO percentages indicate approximate contribution of each LO component to final course grade. (Optional) Assessment provides full coverage of the LO Assessment provides partial coverage of the LO
100%
ECNG6700 Course Plan – (Last Reviewed: 20-Jan-13)
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4
COURSE DELIVERY
4.1
Schedule and Venue
Component Lecture Lab Tutorial Other Activities
4.2 Week
Schedule To be defined None Weekly Numerical Simulation
Venue To be defined
Particulars See the web site of the course. A pass code will be given in course. See the web site of the course.
Target Delivery Schedule Lecture Topics
Learning Resources
LOs Addre ssed4
Other Activities5
Assessment Exercises6 Assigned Due
1-2
Basic elements of probability and random variables: Sample space and events, The notion of axioms of probability, conditional probability, independent events, random variables, distribution functions, mean and variance, some special distributions, Multiple random variables, Joint distributions, Covariance and correlation coefficients; Auto-correlations functions. White noise.
Chapter 1 of Reference 1, Chapter 1, 2 and 3 of Reference 2. Course notes.
LO1
Course work 1 given on week 2.
3-4
Random processes: Introduction; Random processes, Characterization of random processes, Classification of random processes, Poisson processes, Wiener processes, and Markov chains.
Chapter 4 of Ref. 2 and course notes
LO1
Course Work 2 given to the student on week 3.
5-6
Responses of linear systems to stochastic systems: Continuous-time systems, discrete-time systems, Analysis and processing of random processes, Quantification of the power spectral density, Examples.
Chapter 6 of Ref 2 and course notes.
LO2
Course work 1 is discussed in
The course notes are the most important documents to be read carefully.
ECNG6700 Course Plan – (Last Reviewed: 20-Jan-13)
5
course on week 5. 7-9
Estimation theory: Introduction, Parameter estimation, MaximumLikelihood estimation, Mean-Square estimation, Linear Mean-Square estimation, Optimal filter design.
Course Notes. Chapter 7 of Ref. 2.
LO3
10-11
Decision Theory: Introduction, Hypothesis testing, Decisions tests, Map decision rule, Examples.
Course Notes
LO4
12
Stochastical modeling: Introduction, Regressive models, Moving average models, Numerical simulation and design of models using Matlab/Silmulink. Review session and preparation to the final exam.
Course Notes
LO4
13
ECNG6700 Course Plan – (Last Reviewed: 20-Jan-13)
All LOs.
Course Work 3 given to the student on week 9. Work 2 is discussed in course on week 11.
Preparatio n to the final exam. Handling the students issues
Course Work 3 is discussed in course.
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5 5.1
RESOURCES Required Readings 1. Papoulis, A. Probability, Random Variables, and Stochastic Processes, 4nd ed. New York: McGraw-Hill, 2002. 2. Hsu, H. P., Probability, random variables, and random processes, Schaum’s outlines Series, McGraw Hill, 1997.
5.2
Recommended Readings 3. Ross, S. M. Stochastic Processes, 2nd ed. New York: Wiley, p. 59, 1996.
6 6.1
STUDENT CONDUCT Student Attendance
Rule 7 (d) in The Faculty of Engineering: Undergraduate Regulations 2008-2009: “In order for a student to qualify for credit and/or final examination of a course, the student would have had to have a minimum of 75% attendance for that course.” 6.2
Extended Absence from Class
Please note the University’s policy on absence from class as documented in Examination Regulations for First Degrees, Associated Degrees, Diplomas and Certificates 2006/2007: 31. Any candidate who has been absent from the University for a prolonged period during the teaching of a particular course for any reason other than illness or whose attendance at prescribed lectures, classes, practical classes, tutorial, or clinical instructions has been unsatisfactory or who has failed to submit essays or other exercises set by his/her teachers, may be debarred by the relevant Academic, on the recommendation of the relevant Faculty Board, from taking any University examinations. The procedures to be used shall be prescribed in Faculty Regulations. 33. (ii) In cases of illness the candidate shall present to the Campus Registrar…a medical certificate, as proof of illness, signed by the University Health Officer or by another medical practitioner approved for this purpose by the University. The candidate shall send the medical certificate within seven days from the date of that part of the examination in which performance of the candidate is affected. A certificate received after this period will be considered only in exceptional circumstances.
ECNG6700– (Last Reviewed: 20-Jan-13)
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6.3
Missed Coursework Exams Policy
Rule 10 in The Faculty of Engineering: Undergraduate Regulations 2008-2009: “A student who is absent from written coursework tests for grave medical reasons, as prescribed in the University Regulations, shall be graded on the tests he/she has taken as if such tests constitute the full test requirement provided that the tests not taken constitute no more than 20% of the total mark for all the tests7. If the tests not taken constitute more than 20% of the total mark for all the tests, the candidate shall have to take make-up tests at a later date.” 6.4
Coursework Late Submission Policy
According to Rule 11 (b) in The Faculty of Engineering: Undergraduate Regulations 2008-2009, Students are required to submit coursework by the prescribed date. 6.5
Policy on Re-Use of Previous Coursework Grade
Rule 11 (a) in The Faculty of Engineering: Undergraduate Regulations 2008-2009: “Students who fail the examination in any course, but pass the coursework may be exempted from redoing only those sections of the coursework comprising laboratory experiments, workshop and/or field exercises.”
6.6
Statement of Academic Honesty
Academic dishonesty has grave consequences which may include receiving “no grade” on the assignment, debarment from class, or even expulsion from the University. Academic dishonesty is a serious offense which should not be taken lightly. Cheating and plagiarism are both forms of academic dishonesty. Rule 32 in The Faculty of Engineering: Undergraduate Regulations 2008-2009:
“ Cheating, Plagiarism and Collusion are serious offences under University Regulations.
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(a)
Cheating is any attempt to benefit one's self or another by deceit or fraud.
(b)
Plagiarism is the unauthorised and/or unacknowledged use of another person's intellectual efforts and creations howsoever recorded, including whether formally published or in manuscript or in typescript or other printed or electronically presented form and includes taking passages, ideas or structures from another work or author without proper and unequivocal attribution of such source(s), using the conventions for attributions or citing used in this University. Plagiarism is a form of cheating.
20% of entire course weighting. ECNG6700– (Last Reviewed: 20-Jan-13)
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(c)
For the purposes of these Regulations, ‘collusion’ shall mean the unauthorised or unlawful collaboration or agreement between two or more students in the preparation, writing or production of a course assignment for examination and assessment, to the extent that they have produced the same or substantially the same paper, project report, as the case may be, as if it were their separate and individual efforts, in circumstances where they knew or had reason to know that the assignment or a part thereof was not intended to be a group project, but was rather to be the product of each student’s individual efforts. Where two or more students have produced the same or substantially the same assignment for examination and assessment in circumstances that the assignment was to be the product of each student’s individual efforts, they shall receive a failing grade in the course. ”
According to the University of the West Indies’ Code of Principles and Responsibilities for Students, a student may appear before a disciplinary committee for the following misconduct: “Item 5. Presentation of the work of any other person as a student's own work. This includes plagiarism from unpublished and/or electronic sources.”
Every student submission made to the Department of Electrical and Computer Engineering is subject to examination through an electronic plagiarism checker.
ECNG6700– (Last Reviewed: 20-Jan-13)
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