Number of hours
- Lectures 16.5
- Projects -
- Tutorials 12.0
- Internship -
- Laboratory works 4.5
- Written tests -
ECTS
ECTS 3.0
Goal(s)
The objective of this course is two-fold: to provide a comprehensive view on ditributions and Hilbert spaces and then to investigate their use in signal processing.
This course will also contain practical sessions aiming at illustrating the theory with a particular focus on signal processing.
Responsible(s)
Sylvain MEIGNEN
Content(s)
11 courses, 8 practical sessions, 3 sessions on computer
Distributions: convergence, differentiation, multiplication by a function, convolution (3 courses). Hilbert Analysis: Hilbert spaces, projection onto a closed convex set, Hilbert bases (3 courses).
Fourier Transform of Distributions: Reminder on the Fourier transform for functions, on convolution then introduction to the Fourier transform of the distributions
Signal Processing: Shannon Theorem, quantification, Discrete Fourier Transform,
correlation, windowed transforms. Other discrete bases.
Z-transform: Digital Filtering, impulse response, transfer function, RIF and RII filters.
First year course on mathematical analysis
Test
A final examination will take place and the final mark will also involve an evaluation of the
the practical sessions.
- MCC Présentiel **
Examen à la fin du semestre (Note Exam), 3heures
TP (Note TP)
Note finale := (2*Note Exam+Note TP)/3
Examen deuxième session (Note Exam2)
Si examen deuxième session: Note Finale := (2*Note Exam2+Note TP)/3
Calendar
The course exists in the following branches:
- Curriculum - Math. Modelling, Image & Simulation - Semester 7
Additional Information
Course ID : 4MMAFCD6
Course language(s): 
The course is attached to the following structures:
You can find this course among all other courses.
Bibliography
Analyse de Fourier et applications, Editions Masson, Gasquet et Witomski