A vector-space perspective on signal processing. Applications to audio and image processing.
Tuesday and Thursday, 12:30–2:00pm, 2017 ECEB
Instructor: Ivan Dokmanić, dokmanic at illinois dot edu (Office hours: Tuesday 3pm–4pm, 313 CSL)
Teaching assistant: Elad Yarkony, (Office hours: Friday 12-2pm, 5034 ECEB)
August 30, 2018: Elad will be giving a linear algebra review tomorrow in ECEB 3015, from 12 to 2pm
August 28, 2018: Course begins!
All submissions will happen over UofI Box
Link to submission instruction: note the late submission policy!
Week 1 (8/27–8/31): Introduction, signals as vectors, vector spaces
Tuesday slides: Introduction
Thursday slides: Vector spaces, inner products, orthogonality
Notebook: Orthogonality and inner products
Week 2 (9/3–9/7): Hilbert spaces, orthogonal projections, important inequalities
Tuesday slides: Normed spaces, Hilbert spaces, matrix representations of linear operators
Thursday slides: Best linear approximation, orthogonal projections, least squares
Homework assignment 1 (due Thursday, September 13), (solution)
Week 3 (9/10–9/14): Bases and frames; example: Radon transform
Tuesday “slides”: Notebook on bases and frames
Thursday notes: A recap on frames
Homework assignment 2 (due Thursday, September 27), (solution)
Notebook: Frames, noise, and sparsity
Week 4 (9/17–9/21): (Finalize Radon); discrete-domain signals and systems; discrete-time Fourier transform
Tuesday slides (some parts covered last Thursday): Application to Radon transform
Thursday slides: Discrete-domain signal and sytems, DTFT
Notebook: Adventures with the Radon transform
Week 5 (9/24–9/28): z-transform, DTFT, DFT; multirate systems
Tuesday notes (prof. Do) Discrete Fourier Transform, diagonalization of convolution
Thursday notes App: dereverberation via gradient descent; multirate
Notebook: Dereverberation via convolution matrices / gradient descent
Week 6 (10/1–10/5): Multirate systems, polyphase representation, filterbanks
Tuesday notes: Multirate
Thursday notes: Polyphase and filterbanks
Homework assignment 3 (due Wednesday, October 10; __submit 3 out of 5 problems__) (solution)
Midterm 1 (Fall 2015), Midterm 1 (Fall 2016), Practice problem set 1
Week 7 (10/8–10/12): Applications, midterm 1
Tuesday notes: Prony's method
Week 8 (10/15–10/19): Sampling and interpolation
Tuesday notes: Introduction to sampling (Shannon-Nyquist-Whittaker theorem)
Week 9 (10/22–10/26): Generalized sampling and interpolation
Tuesday notes: Generalized sampling 1
Thursday notes: Generalized sampling 2
Homework assignment 4 (due Mon, Nov 5th) solution
Description of project requirements (project proposals due Wednesday, Nov 7th)
Week 10 (10/29–11/2): Finalize sampling, random variables and vectors, linear estimation
Tuesday notes (old): Sampling functions
Thursday: read Section 2.4.4. from VKG + see recap in the next week's Tuesday lecture
Notebook Generalized sampling
Week 11 (11/5–11/9): Linear estimation, discrete random processes, wide-sense stationary, Wiener filter
Tuesday notes: Linear estimation, stochastic processes
Thursday notes: Stochastic processes, Wiener filter
Homework assignment 5 (due Mon, Nov 19th) solution
Week 12 (11/12–11/16): Polynomial approximation and interpolation; splines; applications in filter design; Multiresolution analysis; compressive sensing
Tuesday notes: End of Wiener, beginning of polynomials
Thursday notes: LMS Algorithm
Week 13 (11/19–11/23): Thanksgiving break
Homework assignment 6 (due Sun, Dec 2nd)
Midterm 2 (Fall 2015), Midterm 2 (Fall 2016), Practice problem set 2
Week 14 (11/26–11/30): Compression, transform coding, quantization, Karhunen-Loeve transform, Midterm 2
Week 15 (12/3–12/7): Guest lectures on applications
Homework assignment 7 (Bonus) (due Thu, Dec 13th)
Week 16 (12/10–12/14): Project presentations
30% homeworks
50% midterms
20% final project
Textbook: Vetterli, Kovačević, Goyal, Foundations of Signal Processing, Cambridge University Press, August 2014; online version