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)

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)

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

Week 13 (11/19–11/23): Thanksgiving break

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

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