Fourier analysis - distributions - KAEL7M03

Informations générales

  • Number of hours

    • Lectures 12.0
    • Projects -
    • Tutorials 12.0
    • Internship -
    • Laboratory works -
    • Written tests -

    ECTS

    ECTS 0.3

Goal(s)

manipulate the mathematical tools to understand and solve various problems in signal processing.

Content(s)

FOURIER ANALYSIS : DISTRIBUTIONS

1. Introduction
Test functions
A distribution : what is it ?
Functions as distributions

2. Operations on distributions
Symmetrization and translation of a distribution
Support of a distribution
Multiplication by a smooth function
Differentiation

3. Convergence of a distributions sequence
Limit of a distributions sequence

4. Tempered distributions and Fourier transform of a tempered distribution

5. Convolution of distributions

6. Solving ODE

Prerequisites

Fourier series and transform.

Calendar

The course exists in the following branches:

  • Curriculum - E2I - Semester 7

Additional Information

Course ID : KAEL7M03
Course language(s): FR

You can find this course among all other courses.

Bibliography

Analyse de Fourier et applications, Gasquet, Witomski, Ed. Masson
Distributions et applications, Demengel ; Ed. Ellipses.