Course description

Graduate-level introduction to signal processing with emphasis on vector space methods and adaptive signal processing.

The course prerequisites are undergraduate level probability and DSP. The linear algebra content will be self-contained, though taught at a somewhat fast pace.

Tuesday and Thursday, 12:30–2:00pm, 3081 ECEB 

• Instructor: Farzad Kamalabadi, farzadk [at] illinois [dot] edu

• TBD

Course Overview

This plan will be refined over time.

Time	Topics	Reading
Week 1	Vector Space, Hilbert Space, Linear Operators	[VKG] 1, 2.2, 2.3
Week 2	Projections, Bases, DTFT, Numerical Issues	[VKG] 2.4 - 2.6
Week 3	Discrete-Time Signals	[VKG] 3
Week 4	Multirate and Filterbanks--Midterm I	[VKG] 3.7, 7.2-7.4, Notes
Weeks 5-6	Continuous-Time, Sampling and Interpolation	[VKG] 4,5
Weeks 6-7	Stochastic Processes	[VKG] 3.8, 4.6, Notes
Weeks 7	Estimation	Notes
Weeks 8	Approximation, Splines	[VKG] 6
Week 9	Spring Break	N/A
Week 10	Adaptive Signal Processing	Notes
Week 11-12	Adaptive Signal Processing--Midterm II	Notes
Week 13-14	Special Topics
Weeks 15-16	Final Project Presentations	N/A

Reading

Textbook

• Vetterli, Kovacevic, Goyal, Foundations of Signal Processing, Cambridge University Press, August 2014; online

Alternative Linear Algebra Treatment

• Axler, Linear Algebra Done Right, available as PDF through UIUC online catalog

  • Note: When you search for the book on the library website two links appear. One is broken, the other doesn't seem to properly redirect through the UIUC proxy. Use the above link. If the above link breaks, let us know.

Final Project Details

The final project will focus on your choice of a signal processing paper, with the goal of understanding the work and in some way extending it. The first deadline will be a project proposal, and it will conclude with a write-up and in-class presentation. During this time, the only homework will be to continue working on the final project.

Grading

• 30% Homeworks

• 40% Midterms

• 30% Final Project

Detailed Syllabus

Week 1 (1/19 -- 1/23): Introduction, vector spaces, Hilbert space, and Linear Operators

• Tuesday Lecture (1/20)

  • Reading: [VKG] 1, 2.2,

  • Notes: Introduction

• Thursday Lecture (1/22)

  • Reading: [VKG] 2.2, 2.3

  • Notes: Inner Products, Norms, Hilbert Spaces, Linear Operators

Week 2 (1/26 - 1/30): Projections (continued), Bases, Numerical Issues

• Assignment 1 (Due 9/3) 

• Tuesday Lecture (1/27)

  • Reading: 2.4, 2.5

  • Notes: Projections and Bases

• Thursday Lecture (1/29)

  • Reading: 2.5, 2.6, 3.3

  • Notes: Bases, Numerical Issues, and Discrete-Time Systems