Course EE621: Modeling and Analysis of Random Signals

Instructor: Prof. Abhishek Gupta, EE, Indian Institute of Technology, Kanpur

Course Details

Per Week: 2 Lectures, 3 Hours, Pre-recorded, Released on MooKit
Discussion Class: W 12pm-1 pm ()
Credits: 9
Duration of Course: Full Semester.

Instructor's Office Hours: Wednesday 12-1PM

Teaching Assistants:

• Nithin VS. Email: nithinvs[AT]iitk.ac.in
• Kaushelndra Pandey. Email: kpandey[AT]iitk.ac.in
• Surendra. Email: skota[AT]iitk.ac.in
• Shuchi Tripathi. Email: shuchi[AT]iitk.ac.in
• Office Hours: TBD

Course Description:

Objective: This course will focus on strengthening foundation of probability keeping its application into signal processing and communications in mind. The course is divided into two parts. First part would discuss probability space, random variables and their transformations, conditional distributions and estimation of random variables. Second part will extend the theory to random vectors, random processes including Markov chains and some applications into linear systems. After completion of the course, the students should be able to strengthen their base in probability theory and stochastic processes and apply these tools in their own research.

Pre-requisite: Basic Probability, Basic Calculus

Recommended books:

• Papoulis, ``Probability, Random Variables, and Stochastic Processes,'' McGraw-Hill
• Bruce Hajek, ``An Exploration of Random Processes for Engineers'' Online
• Class notes.

Course Policy

Online Quizes/Other Online Evaluations	35
Mid-sem exam	15
End-sem exam	20
Assignments	30

Note:

• Assignments may contain some programming/coding tasks. Students are expected to learn MATLAB by themselves. (MATLAB is very easy language and will also help in further research.)
• Use of unfair means is not allowed in any case.
• In case you take help of each other in assignments or discuss in groups, you must write the name of everyone in top while submitting the assignment. It will not affect your grades. However, assignments problems should be solved finally by yourself and not just copied from others.

Course Contents (tentative)

• Introduction to Probability
• Review of set theory, real analysis
• Cardinality and Countability
• Probability Space
• Discreet Probability space
• Continuous Probability space
• Conditional Probability and Independence
• Random Variable
• Continuous and Discreet Random Variable
• Distribution: CDF and PDF/PMF
• Random Variable Transformation
• Functions of Random Variables
• Measures of Random Variable: Expectation, Variance
• Conditional Expectation
• Characteristic functions, Laplace, MGF
• Convergence of RVs, Law of Large Number, CLT
• Concentration Inequalities
• Random Process
• Examples
• Measures of Random Process
• Properties of Random Process
• Discreet time markov chain (DTMC)