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, Online

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

• Teaching Assistant: Helmuth Naumer, hnaumer2 [at] illinois [dot] edu

Announcements

Office Hours Information here

Lecture recordings available here

Submit Homework on Compass

Midterm Solution

Lecture 22 Notes PDF

Lecture 21 Notes PDF

Lecture 19 Notes PDF

Homework 7 Solution Available!

Homework 9 Posted! PDF, LaTeX

Lecture 18 Notes (annotated) PDF

Lecture 17 Notes PDF

Homework 8 Posted! PDF, LaTeX, and image

Lecture 16 Notes (annotated) PDF

Lecture 15 Notes (annotated) PDF and Dynamic Gain Plot and Static Gain Plot

Midterm Details

The exam has been distributed over email.

Solution

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 due on November 5th, and it will conclude with a write-up and in-class presentation after Fall break (starting December 1st).

During this time, the only homework will be to continue working on the final project.

Details regarding the project are available here

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	[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	Adaptive Signal Processing	Notes
Week 10	Midterm (10/29)
Week 11-13	Special Topics	Notes
Week 14	Fall Break
Weeks 15-16	Final Project Presentations	N/A

Reading

Textbook

• Vetterli, Kovačević, 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.

Grading

• 40% Homeworks

• 30% Midterm

• 30% Final Project

Detailed Syllabus

Week 1 (8/24 – 8/28): Introduction, vector spaces, Hilbert space, and Linear Operators

• Assignment 1 (Due 9/3) Solution

• Tuesday Lecture (8/25)

  • Reading: [VKG] 1, 2.2,

  • Notes: Introduction

• Tuesday Lecture (8/27)

  • Reading: [VKG] 2.2, 2.3

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

Week 2 (8/31 - 9/4): Projections (continued), Bases, Numerical Issues

• Assignment 2 (Due 9/10) Solution

• Tuesday Lecture (9/1)

  • Reading: 2.4, 2.5

  • Notes: Projections and Bases

• Thursday Lecture (9/3)

  • Reading: 2.5, 2.6, 3.3

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

Week 3 (9/7 - 9/11):

• Assignment 3 (Due 9/17) Solution

• Tuesday Lecture (9/8)

  • Reading: 3.3

  • Notes: Discrete-Time Systems and DTFT

• Thursday Lecture (9/10)

  • Reading: 3.4, 3.5, 3.6, 3.7

  • Notes: DTFT, Allpass Filters, Z-Transforms

Week 4 (9/14 - 9/18):

• Assignment 4 (Due 9/24) Solution PDF and code

• Tuesday Lecture (9/15)

  • Reading: 3.7, 4.4, 7.2

  • Notes: Multirate (No Buttons)

• Thursday Lecture (9/17)

  • Reading: 4.4, 7

  • Notes:Uncertainty, STFT, and Filter Banks

Week 5 (9/21 - 9/25):

• Assignment 5: PDF, Source(Due 8/1) Solution

• Tuesday Lecture (9/22)

  • Reading: 5

  • Notes: Sampling

• Thursday Lecture (9/24)

  • Reading: 5

  • Notes: Sampling Continued

Week 6 (9/28 - 10/2):

• Assignment 6: PDF, Source and Photos(Due 8/8) Solution (code))

• Tuesday Lecture (9/29) Radon Transform

  • Reading:

  • Notes: Handwritten Notes to be Uploaded Later

• Thursday Lecture (10/1)

  • Reading:

  • Notes: Stochastic Processes

Week 7 (10/5 - 10/9):

• Assignment 7: PDF, Source and Audio(Due 8/15) Solution

• Tuesday Lecture (10/6)

  • Reading:

  • Notes: Estimation

• Thursday Lecture (10/8)

  • Reading:

  • Notes: Estimation (part 2)

Week 8 (10/12 - 10/16):

• PDF (Due 8/22) , LaTeX, and image

• Tuesday Lecture (10/13)

  • Reading:

  • Notes: (annotated) PDF and Dynamic Gain Plot and Static Gain Plot

• Thursday Lecture (10/15)

  • Reading:

  • Notes: (annotated) PDF

Week 9 (10/19 - 10/23):

• PSET 9 pdf, LaTeX (No Images) Due (10/29)

• Tuesday Lecture (10/20)

  • Reading:

  • Notes:PDF

• Thursday Lecture (10/22)

  • Reading:

  • Notes: (annotated) PDF

Week 10 (10/26 - 10/30):

• Tuesday Lecture (10/27)

  • Reading: Chapter 6

  • Notes: PDF

• Thursday Lecture (10/29)

  • Reading:

  • Notes:

Week 11 (11/2 - 11/6):

• Tuesday Lecture (11/3)

  • Reading:

  • Notes:

• Thursday Lecture (11/5)

  • Reading:

  • Notes:

Week 12 (11/9 - 11/13):

• Tuesday Lecture (11/10)

  • Reading: Chapter 6

  • Notes: PDF

• Thursday Lecture (11/12)

  • Reading:

  • Notes: PDF

Week 13 (11/16 - 11/20):

• Tuesday Lecture (11/3)

  • Reading:

  • Notes:

• Thursday Lecture (11/5)

  • Reading:

  • Notes:

Week 14 (11/23 - 11/27):

• Fall Break

Week 15 (11/30 - 12/4):

• Tuesday Lecture (12/1)

  • Final Project Presentations

• Thursday Lecture (12/3)

  • Final Project Presentations

Week 16 (12/7 - 12/9):

• Tuesday Lecture (12/1)

  • Final Project Presentations