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 1B Programming in Python (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 Chapter
1 — 01/27 Lecture 0, Lecture 1 Course Overview, Basic Concepts in Probability, Probability Models 1
2 — 02/03 Lecture 2 Review of Probability: Set theory, Probability Spaces 2
3 — 02/10 Lecture 2, Lecture 2A Computing Probabilities Using Counting Methods, Replacement, and Ordering 2
4 — 02/17 Lecture 3 Conditional Probability, Bayes' Rule, Independence, Generation of Random Numbers 2
5 — 02/24 Lecture 3 More on Bayes' Rule, Independence, and Real-World Examples 2
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 Variable 3
7 — 03/10 Mid-Term Exam
8 — 03/17 Spring Break
9 — 03/24 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 3
10 — 03/31 Lecture 5 Continuous Random Variables: Cumulative Distribution Functions (CDF), Probability Density Functions (PDF), Moment of a Random Variable, Mean and Variance of Continuous Random Variables 4
11 — 04/07 Lecture 6 Discrete Random Variables: Cumulative Distribution Functions (CDF), Probability Mass Functions (PMF), Mean and Variance of Discrete Random Variables 4
12 — 04/14 Lecture 6 Functions of Random Variables, Expectations and Characteristic Function, Markov and Chebychev Inequalities 4
13 — 04/21 Lecture 7 Two Random Variables: Marginal Probability Mass Function, Joint CDF, Joint PDF, Conditional Distributions and Independence, Expected Value of a Function of Two Random Variables, Expectations and Correlations, Pairs of Jointly Gaussian Random Variables, Generating Jointly Gaussian Random Variable 5
14 — 04/28 Lecture 8 Random Vectors: Functions of Several Random Variables, Expected Value of Vector Random Variables, Jointly Gaussian Random Vectors, and Convergence of Random Sequences 6
15 — 05/05 Lecture 9 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 9
16 — 05/12 Final Exam

Last day of class is May 9, 2025.