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Lahore University of Management Sciences
EE564 – Stochastic SystemsFall 2014
Instructor Momin Uppal
Room No. 9-346A
Office Hours TBA
Email [email protected]
Telephone 8112
Secretary/TA TBA
TA Office Hours TBA
Course URL (if any)
Course Basics
Credit Hours 3
Lecture(s) Nbr of Lec(s) Per Week 2 Duration 75
minutesRecitation/Lab (per week) Nbr of Lec(s) Per Week 0
Duration
Tutorial (per week) Nbr of Lec(s) Per Week 1 Duration 60
minutes
Course Distribution
Core MS Electrical Engineering, Areas 1, 6, 7, and 8.
Elective MS Electrical Engineering, all other areas, BS
Electrical Engineering
Open for Student Category Anyone with the required
pre-requisite
Close for Student Category Anyone not fulfilling the required
pre-requisite
COURSE DESCRIPTION
This is a first-year graduate level course in probability,
random variables, and random processes. Besides fundamental
concepts in random
variables, density functions, and expectations, the course will
also include coverage of random vectors and random
signals/processes along with
an emphasis on response of linear time-invariant systems to
random inputs. The course contents will be complemented with
important
applications of these concepts to diverse areas of electrical
engineering including, but not limited to, communication systems,
communication
networks, control systems, and signal processing
applications.
COURSE PREREQUISITE(S)
MATH 230 - Probability (or an equivalent undergraduate
probability course)
Sound background in undergraduate-level probability, calculus,
and linear algebra.
COURSE OBJECTIVES
To gain fundamental understanding of concepts in random
variables and random processes.
To gain an understanding of how linear-time invariant systems
respond to random inputs.
To gain knowledge of a fundamental toolset that could be
utilized to design and analyze (in the face of unavoidable
randomness) communication systems, communication networks,
control systems, and signal processing systems
mailto:[email protected]:[email protected]:[email protected]
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Lahore University of Management Sciences
Learning Outcomes
By the end of the course, the students will
Have a fundamental understanding of probability, random
variables, and random processes.
Have an understanding of how linear time-invariant systems
behave under random inputs.
Be able to apply the techniques learnt in class to incorporate
unavoidable randomness in the design and analysis of systems in
diverse areas of electrical engineering.
Grading Breakup and Policy (Tentative)
Assignment(s): 10%
Home Work:
Quiz(s): 20%
Class Participation:
Attendance:
Midterm Examination:30%
Project:
Final Examination:40%
Examination Detail (Tentative)
Midterm
Exam
Yes/No: Yes
Combine Separate: Combined
Duration: 3 hours
Preferred Date: During the Midweek
Exam Specifications: Closed book closed notes/Calculators
Allowed
Final Exam
Yes/No: Yes
Combine Separate: Combined
Duration: 3 hoursExam Specifications: Closed book closed
notes/Calculators Allowed/ Two help sheets Allowed
Textbook(s)/Supplementary Readings
Text. Probability and Random Processes with Applications to
Signal Processing, by Henry Stark and John Woods.
Reference. Probability and Random Processes, by Scott
Miller and Donald Childers.
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Lahore University of Management Sciences
Week TopicsRecommended
Readings
1 Course Overview
1
Basic probability theory
Joint and conditional probability
Baye's rule
Independence
2
Discrete random variables
Probability mass functions
Common discrete random variables
3
Continuous random variables
Cumulative distribution functions
Probability density functions,
Conditional distribution and density functions
Common continuous random variables
4
Pairs of Random Variables
Joint and conditional PMFs, CDFs, and PDFs
Transformation of random variables
5-6
Expectations
Expected values
Moments
Conditional Expected values
Characteristic Functions
Moment generating functions
Evaluating tail probabilities
MMSE estimation
7
Random Vectors and Parameter Estimation
Joint and conditional PMFs, CDFs, and PDFs
Expectation vectors and covariance matrices
Multidimensional Gaussian Law
Parameter estimation
8-9
Random Sequences
Basic Concepts
Markov Random Sequences
Law of large numbers
Convergence of random sequences
10-11
Random Processes
Basic Concepts
Stationary and Ergodic Random processes
Important Random Processes (Gaussian, Poisson etc.)
12
Power Spectral Density
Basic Concepts
Bandwidth of a random process
13-14
Random Processes in Linear Systems
LTI filtering of stationary processes
The matched filter
The Weiner Filter
