# Fiches de cours

## Signals and systems (for EL&IC)

#### Enseignant(s) :

Shkel Yanina Yurina

English

#### Summary

This class teaches the theory of linear time-invariant (LTI) systems. These systems serve both as models of physical reality (such as the wireless channel) and as engineered systems (such as electrical circuits, filters and control strategies).

#### Content

The design of advanced systems (such as WiFi, cell phones, drones, airplanes) requires a thorough theoretical underpinning. This class teaches one of the most powerful and important pillars: The theory of linear time-invariant (LTI) systems. These systems serve both as models of physical reality (such as the wireless channel) and as engineered systems (such as filters and control strategies).

The class will cover the following topics :

1. Systems: Definitions (1 week)
2. LTI Systems (3 weeks)
3. The Frequency Response of stable LTI Systems (1 week)
4. Fourier Techniques for stable LTI Systems (3 weeks); with applications to Communication Systems and Signal Processing
5. Laplace and Z-Transform Techniques for LTI Systems (5 weeks); with applications to Control Systems

#### Keywords

Systems, Circuits, Signals, Frequency Response, Transfer Function, Fourier Transform, Laplace Transform, Z Transform, Stability, Causality, Sampling

#### Learning Prerequisites

##### Required courses

Analysis I, II, III. Linear algebra I.

##### Recommended courses

Linear algebra II

#### Learning Outcomes

By the end of the course, the student must be able to:
• Describe properties of LTI systems
• Solve for poles and zeros of LTI systems
• Recall properties of CT Fourier transform
• Analyze LTI systems by spectral analysis
• Operate with Fourier transform tools
• Work out / Determine impulse response of CT LTI

#### Teaching methods

• Classroom lectures
• Written exercises

#### Expected student activities

• Read course book in english (the course is taught in english)

#### Assessment methods

Homeworks and written mid-term exam and final exams

#### Resources

##### Bibliography

The following is a recommended (but not required) book:

A. V. Oppenheim and A. S. Willsky, with S. Hamid Nawab, Signals and Systems. Upper Saddle River, NJ: Prentice Hall, 2nd ed., 1996.

### Dans les plans d'études

• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
4
• Matière examinée
Signals and systems (for EL&IC)
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
4
• Matière examinée
Signals and systems (for EL&IC)
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Passerelle HES - EL, 2020-2021, Semestre printemps
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
4
• Matière examinée
Signals and systems (for EL&IC)
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Passerelle HES - SC, 2020-2021, Semestre printemps
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
4
• Matière examinée
Signals and systems (for EL&IC)
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
4
• Matière examinée
Signals and systems (for EL&IC)
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines
• Semestre
Printemps
• Forme de l'examen
Ecrit
• Crédits
4
• Matière examinée
Signals and systems (for EL&IC)
• Cours
2 Heure(s) hebdo x 14 semaines
• Exercices
2 Heure(s) hebdo x 14 semaines

### 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