Download Course Syllabus 18-751 SV: Fall, 2014

Course Syllabus
18-751 SV: Applied Stochastic Processes
Fall, 2014
Instructor: Osman Yagan
Office: B23 Room 221
Email: [email protected]
Office Hours: Wednesday 1-2pm
Teaching Assistant: Avneesh Saluja
Office: B19 Room 1031
Email Address: [email protected]
Office Hours: Friday 1-3pm
Academic Services Assistant: Stephanie Scott
Email: [email protected]
Office Location: B19 Room 1052
Course Description: We introduce random processes and their applications. Throughout
the course, we mainly take a discrete-time point of view, and discuss the continuous-time
case when necessary. We first introduce the basic concepts of random variables, random
vectors, stochastic processes, and random fields. We then introduce common random
processes including the white noise, Gaussian processes, Markov processes, Poisson
processes, and Markov random fields. We address moment analysis (including KarhunenLoeve transform), the frequency-domain description, and linear systems applied to
stochastic processes. We also present elements of estimation theory and optimal filtering
including Wiener and Kalman filtering. Advanced topics in modern statistical signal
processing such as linear prediction, linear models and spectrum estimation are
discussed. 4 hrs. lec.
Number of Units: 12
Pre-requisites: 36-217 and 18-396 and senior or graduate standing.
It is strongly advised that students have a prior Signals and Systems course and a
Probability course.
Graduate Course Area: Signals and Systems, Signal Processing and Communications
Class Schedule:
• Lecture:
Mondays and Wednesdays 10:00 am–11:50 pm, Silicon Valley campus B23 RM
212 (4 hours per week)
•
Recitations
Fridays 10 am -11:50 am Silicon Valley campus B23 RM212 (2 hours per week)
Required Textbook:
• Probability, Random Variables, and Stochastic Processes. Papoulis, S. U. Pillai.
2001. ISBN-13: 9780071122566
Recommended supplementary readings:
• R. Gallager, Stochastic Processes: Theory for Applications, Draft available online
• A. Leon-Garcia, Probability and Random Processes for Electrical Engineering,
2nd ed., Prentice Hall, 1993.
• C.W. Helstrom, Probability and Stochastic Processes for Engineers, 2nd ed.,
Prentice Hall, 1990.
Course Web Page: www.ece.cmu.edu/~oyagan/current-course.html
Course Blackboard: To access the course blackboard from an Andrew Machine, go to
the login page at: http://www.cmu.edu/blackboard. You should check the course
blackboard daily for announcements and handouts.
Course Wiki:
Students are encouraged to use the ECE wiki to provide feedback about the course at:
http://wiki.ece.cmu.edu/index.php.
Grading Algorithm:
Course evaluation will be based on 3 tests, 5 quizzes, and homework. The contribution of
these components will be as follows:
Homework (Best 9 out of 10 sets)
Quizzes (5 sets)
Test (3 tests, 20% each)
25%
15%
60%
Tentative schedules:
Test #1: September 29th, Monday
Test #2: October 29th, Wednesday
Test #3: December 3rd, Wednesday
Date
August
8/25
Day
Mon
8/27
Wed
September
Class Activity
Review of course content. Definitions of probability experiments,
sample space, event space and prob. measure, conditional probability.
Law of total probability, Bayes’ Theorem, independence of events;
Events that occur “infinitely often” and “eventually”, Borel-Cantelli
Lemmas
2
9/1
Mon
9/3
Wed
9/8
Mon
9/10
Wed
9/15
Mon
9/17
Wed
9/22
Mon
9/24
Wed
9/29
Mon
October
10/1
10/6
Wed
Mon
10/8
Wed
10/13
Mon
10/15
Wed
10/20
Mon
10/22
Wed
10/27
Mon
10/29
Wed
November
Labor Day - NO CLASSES
Definition of a random variable (discrete and continuous), distribution of
a random variable (cdf and pdf), commonly used random variables
Joint density of two or more random variables and their properties,
random vectors, Conditional distribution/density, Bayes’ rule for pdfs,
chain rule for densities,
Quiz 1. Independence of random variables, Functions of random
variables.
Two functions of two random variables (and deriving their joint
density). Order statistics, Mean, variance and other moments.
Conditional Mean. Covariance, correlation coefficient.
Markov inequality, Chebyshev inequality, and Chernoff bound, Joint
moments, covariance matrices. Characteristic function.
Quiz 2. Moment Generating Function, Probability Generating Function.
MMSE Estimation: definition and estimation by a constant
MMSE Estimation: linear, and unconstrained; Orthogonality principle.
Test 1
Convergence of sequence of real numbers, convergence of random
variables (almost surely, r^th mean, in probability, in distribution)
Law of large numbers (Weak and Strong) and Central Limit Theorem
Convergence of Binomial Distribution to Poisson. Bivariate Normal
random variables
Quiz 3. Multi-variate Normal Random Variables, PDF, Covariance
Matrix, Characteristic Function, and properties.
Transformation of Correlated Random variables into Uncorrelated ones.
Discrete-time Markov Chains, definitions, examples. Time-homegenous
Markov Chains, Transition probability matrix.
Markov Chains cont’d: Recurrence time, transient and recurrent states,
classification of states (open, closed).
Period of a state, stationary distributions, irreducible and reducible
Markov chains, ergodicity.
Quiz 4. Review before Test 2.
Test 2
11/3
Mon
11/5
Wed
11/10
11/12
Mon
Wed
Random processes, definitions, mean, auto-correlation, and autocovariance function. First and higher order density of random processes.
Independent and Stationary Increments Property. Gaussian random
process, Brownian motion.
Counting processes and Poisson Process. Strict Sense Stationarity, Wide
Sense Stationarity.
Cross-correlation and cross-covariance, Cyclo-stationary processes,
Random processes in linear systems. WSS processes in LTI systems.
Power Spectral Density, Properties, Examples
Mon
Wed
Discrete Random Processes in LTI systems. Ergodicity, mean
ergodicity, ergodicity with respect to the first and second order density
function.
Quiz 5. No class – Qual week
11/17
11/19
11/24
Mon
11/26
Wed
December
12/1
Mon
Wiener Filtering, and its general solution. Statement of the causal linear
Wiener Filtering Problem, Wiener – Hopf equations. Causal functions
and spectral factorization.
Thanksgiving Break - NO CLASSES
Spectral factorization cont’d. Multiplicative decomposition. Solution of
the causal Wiener Filtering problem for rational PSD’s.
12/3
12/8 12/15
Wed
Test 3
Mon
Final Exams
Education Objectives (Relationship of Course to Program Outcomes)
** Keep only those that apply and append a brief description of what is done in the
course do address each outcome
(a) an ability to apply knowledge of mathematics, science, and engineering:
<<description of how this course achieves the objective>>
(b) an ability to design and conduct experiments, as well as to analyze and
interpret data:
<<description of how this course achieves the objective>>
(e) an ability to identify, formulate, and solve engineering problems:
<<description of how this course achieves the objective>>
(f) an understanding of professional and ethical responsibility:
<<description of how this course achieves the objective>>
(h) the broad education necessary to understand the impact of engineering
solutions in a global, economic, environmental, and societal context:
<<description of how this course achieves the objective>>
(i) a recognition of the need for, and an ability to engage in life-long
learning
<<description of how this course achieves the objective>>
(j) a knowledge of contemporary issues:
<<description of how this course achieves the objective>>
(k) an ability to use the techniques, skills, and modern engineering tools
necessary for engineering practice:
<<description of how this course achieves the objective>>
Academic Integrity Policy (http://www.ece.cmu.edu/student/integrity.html):
The Department of Electrical and Computer Engineering adheres to the academic
integrity policies set forth by Carnegie Mellon University and by the College of
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Engineering. ECE students should review fully and carefully Carnegie Mellon
University's policies regarding Cheating and Plagiarism; Undergraduate Academic
Discipline; and Graduate Academic Discipline. ECE graduate student should further
review the Penalties for Graduate Student Academic Integrity Violations in CIT outlined
in the CIT Policy on Graduate Student Academic Integrity Violations. In addition to the
above university and college-level policies, it is ECE's policy that an ECE graduate
student may not drop a course in which a disciplinary action is assessed or pending
without the course instructor's explicit approval. Further, an ECE course instructor may
set his/her own course-specific academic integrity policies that do not conflict with
university and college-level policies; course-specific policies should be made available to
the students in writing in the first week of class.
This policy applies, in all respects, to this course.
Carnegie Mellon University's Policy on Cheating and Plagiarism
(http://www.cmu.edu/policies/documents/Cheating.html) states the following,
Students at Carnegie Mellon are engaged in preparation for professional activity
of the highest standards. Each profession constrains its members with both ethical
responsibilities and disciplinary limits. To assure the validity of the learning
experience a university establishes clear standards for student work.
In any presentation, creative, artistic, or research, it is the ethical responsibility of
each student to identify the conceptual sources of the work submitted. Failure to
do so is dishonest and is the basis for a charge of cheating or plagiarism, which is
subject to disciplinary action.
Cheating includes but is not necessarily limited to:
1. Plagiarism, explained below.
2. Submission of work that is not the student's own for papers, assignments
or exams.
3. Submission or use of falsified data.
4. Theft of or unauthorized access to an exam.
5. Use of an alternate, stand-in or proxy during an examination.
6. Use of unauthorized material including textbooks, notes or computer
programs in the preparation of an assignment or during an examination.
7. Supplying or communicating in any way unauthorized information to
another student for the preparation of an assignment or during an
examination.
8. Collaboration in the preparation of an assignment. Unless specifically
permitted or required by the instructor, collaboration will usually be
viewed by the university as cheating. Each student, therefore, is
responsible for understanding the policies of the department offering any
course as they refer to the amount of help and collaboration permitted in
preparation of assignments.
9. Submission of the same work for credit in two courses without obtaining
the permission of the instructors beforehand.
Plagiarism includes, but is not limited to, failure to indicate the source with
quotation marks or footnotes where appropriate if any of the following are
reproduced in the work submitted by a student:
1. A phrase, written or musical.
2. A graphic element.
3. A proof.
4. Specific language.
5. An idea derived from the work, published or unpublished, of another
person.
This policy applies, in all respects, to 18-751 SV.
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