# Fiches de cours

## Mathematical foundations of signal processing

#### Enseignant(s) :

Kolundzija Mihailo
Parhizkar Reza

English

#### Summary

Signal processing tools are presented from an intuitive geometric point of view which is at the heart of all modern signal processing techniques. Student will develop the mathematical depth and rigor needed for the study of advanced topics in signal processing.

#### Content

From Euclid to Hilbert applied to inverse problems (vector spaces; Hilbert spaces; approximations, projections and decompositions; bases)

Sequences, Discrete-Time Systems, Functions and Continuous-Time Systems (flipped class review of discrete-time Fourier transform; z-transform; DFT; Fourier transform and Fourier series).

Sampling and Interpolation (sampling and interpolation with finite-dimensional vectors, sequences and functions)

Approximation and compression (polynomial and spline approximation, transform coding and compression)

Localization and uncertainty (time and frequency localization for sequences and functions, tiling the time-frequency plane)

Computerized tomography fundamentals (line integrals and projections, Radon transform, Fourier projection/slice theorem, filtered backprojection algorithm, algebraic reconstruction techniques).

Array signal processing fundamentals (spatial filtering and beamforming, adaptive beamforming, acoustic and EM source localization techniques).

Compressed sensing and finite rate of innovation (overview and definitions, reconstruction methods and applications)

Euclidean Distance Matrices (definition, properties and applications).

#### Learning Prerequisites

##### Required courses

Circuits and Systems

Signal processing for communications (or Digital signal processing on Coursera)

#### Learning Outcomes

By the end of the course, the student must be able to:
• Master the right tools to tackle advanced signal and data processing problems
• Develop an intuitive understanding of signal processing through a geometrical approach
• Get to know the applications that are of interest today
• Learn about topics that are at the forefront of signal processing research

#### Teaching methods

Ex cathedra with exercises

One week of flipped class

#### Expected student activities

Attending lectures, completing exercises

#### Assessment methods

Homeworks 20%, midterm (written) 30%, final exam (written) 50%

#### Supervision

 Office hours Yes Assistants Yes Forum No

#### Resources

No

##### Bibliography

M. Vetterli, J. Kovacevic and V. Goyal, "Signal Processing: Foundations", Cambridge U. Press, 2014.

Available in open access at http://www.fourierandwavelets.org

### Semaine de référence

LuMaMeJeVe
8-9
9-10
10-11
11-12
12-13
13-14
14-15INM203
15-16INM203   INM203
16-17
17-18
18-19
19-20
20-21
21-22

Cours
Exercice, TP
Projet, autre

### légende

• Semestre d'automne
• Session d'hiver
• Semestre de printemps
• Session d'été
• Cours en français
• Cours en anglais
• Cours en allemand