# Fiches de cours 2017-2018

## 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 (vector spaces; Hilbert spaces; approximations, projections and decompositions; bases)

Sequences and Discrete-Time Systems (sequences; systems; discrete-time Fourier transform; z-transform; DFT; multirate sequences and systems; filterbanks)

Functions and Continuous-Time Systems (functions; systems; Fourier transform; Fourier series)

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

Approximation and Compression (approximation by polynomials, splines, and series truncation)

Localization and Uncertainty (localization for functions, sequences and bases; local Fourier and wavelet bases; time, frequency and resolution in the real world)

Compressed Sensing (overview and definitions; reconstruction methods and applications)

#### Learning Prerequisites

##### Required courses

Circuits and Systems

##### Recommended courses

Signal processing for communications

#### 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

#### 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
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
En construction

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