ENEM 603: Random Signals Analysis

Instructor:

Liang Zhang, Assistant Professor

Prerequisites

ENGE 320 (all with grade of C or better), or permission of instructor.

Objectives

This course provides basic theory and important applications. Topics include probability concepts and axioms; stationarity and ergodicity; random variables and their functions; vectors; expectation and variance; conditional expectation; moment-generating and characteristic functions; random processes such as white noise and Gaussian; autocorrelation and power spectral density; linear filtering of random processes, and basic ideas of estimation and detection.

Location

EASC 1064

Time

Mon/Wed/Fri 4:00-4:50 pm

ENEM 603 Syllabus

ENEM 603 Lecture Notes

Lectures Download Links
Lecture 0 Lecture 0 (pdf)
Lecture 1 Lecture 1 (pdf)
Lecture 2 Lecture 2 (pdf)
Lecture 3 Lecture 3 (pdf)
Lecture 4 Lecture 4 (pdf)
Lecture 5 Lecture 5 (pdf)
Lecture 6 Lecture 6 (pdf)
Lecture 7 Lecture 7 (pdf)
Lecture 8 Lecture 8 (pdf) Video part 1 (mp4) Video part 2 (mp4)
Lecture 9 Lecture 9 (pdf)
Annex (Generating RVs) Annex (pdf)
Lecture 10 Lecture 10 (pdf)
Lecture 11 Lecture 11 (pdf)
Lecture 12 Lecture 12 (pdf)
Lecture 13 Lecture 13 (pdf)
Lecture 14 Lecture 14 (pdf)
Lecture 15 Lecture 15 (pdf)
Lecture 16 Lecture 16 (pdf)
Formula Sheetpmf and pdf for exam

Projects

  1. Project 1

    Project     Solutions

  2. Project 2

    Project     Solutions

  3. Project 3

    Project     Solutions

Homework

Course Schedule

Week Lecture Topic
1, 01/27 Lecture 0, Lecture 1, HW1 Course overview, basic concepts in probability, Probability Models in ECE (chapter 1)
2, 02/03 Lecture 2, Review of probability: set theory, probability spaces
3, 02/10 Lecture 2, HW2 Review of probability: set theory, probability spaces
4, 02/17 Lecture 3 More on conditional probability, Bayes' Rule, independence, more on the generation of random numbers
5, 02/24 Lecture 3 More on conditional probability, Bayes' Rule, independence, more on the generation of random numbers
6, 03/03 Lecture 4 Discrete Random Variables: Notion of a Random Variable, Probability Mass Functions (PMF), Expected Value, Moments, Important Discrete Random Variables, Generation of Discrete Random Variables
7, 03/10 midddle exam and Lecture 5 General Random Variables (Single Variable): Cumulative Distribution Functions (CDF), Probability Density Functions (PDF), functions of random variables, expectations and characteristic function, Markov and Chebychev inequalities
8, 03/17 Lecture 6 General Random Variables (Single Variable): Cumulative Distribution Functions (CDF), Probability Density Functions (PDF), functions of random variables, expectations and characteristic function, Markov and Chebychev inequalities
9, 03/24 Lecture 7 Pairs of Random Variables: joint and marginal distributions, conditional distributions and independence, functions of two random variables, Expectations and correlations, pairs of jointly Gaussian Random Variables, generating jointly Gaussian Random Variables (chap 5)
10, 03/31 Lecture 8 Random vectors: Functions of several random variables expected value of vector random variables, jointly Gaussian Random vectors, convergence of random sequences (chap 6)
11, 04/07 Lecture 8 Random vectors: Functions of several random variables expected value of vector random variables, jointly Gaussian Random vectors, convergence of random sequences (chap 6)
12, 04/14 Lecture 9 Sums of random variables and long-term averages: the sample mean and the Laws of Large Numbers, the Central Limit Theorem (chap 7)
13, 04/21 Lecture 10 Stochastic Processes: Basic concepts, Covariance, correlation, and stationarity, Gaussian processes and Brownian motion, Poisson and related processes, Power spectral density, Stochastic processes and linear systems (chap 9)
14, 04/28 Lecture 11 Stochastic Processes
15, 05/05 Lecture 12 Markov Processes and Markov Chains (chap 11) - Last Class
16, 05/12 Final Exam

Last day of class is May 9, 2025.