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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.
12 courses, 7 practical sessions, 5 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 cours).
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, transfert function,,RIF and RII filters.
First year course on mathematical analysis
A final examination will take place and the final mark will also involve an evaluation of the
the practical sessions.
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
Analyse de Fourier et applications, Editions Masson, Gasquet et Witomski