5PMSRSM6 : Signal Representations and Models - WPMTDSR0

Goal(s)

OBJECTIVES:
Many signals (acoustics, natural, vibratory, mechanical, etc.) are or comprise a nonstationary part. To describe these nonstationary signals, one must use time-frequency and/or time-scale representations. The objective of this course will be to understand and know to use time-frequency and time-scale tools making it possible to avoid the rigid framework of Fourier analysis.

LEVEL:
Advanced course for Bac +5/ 3A Engineerinf School. This course is also open to the students of Master.

TEXTBOOKS:
Flandrin P.,Temps Fréquences, Traité des nouvelles technologies, Série Traitement du Signal, Hermès, 1993
Chui C.K., An introduction to wavelets (Vol. 1), Wavelets – a Tutorial in theory and applications (Vol. 2), Wavelet analysis and its application, Academic Press, New York. 1992

LEARNING METHOD(S):
Language: French / English
Working session: lectures,
Personal work: Preparation

Content(s)

CONTENTS: 14 h lectures
Part 1: Lectures on Time frequency representation
Stationary and non stationary description, Time frequency uncertainty, Instantaneous time frequency representation, Wigner Ville distribution and its different approaches, Ambiguity function, Spectrogram, Empirical mode decomposition; Time frequency representation based on modelisation approaches,
Part 2: Lectures on Wavelet transforms (continuous, discrete, 1D, 2D etc) – Bilinear representation – Time frequency time space reconstruction.

Labworks : 8 h
Application: time frequency / time scale analysis on non stationary signals, Denoising. Application on real signal (dolphins).

PREREQUISITES:
Basis of Signal Processing (Fourier analysis and spectral analysis)

Test

Semester 9 - The exam is given in english only 

Examination 2h + Continuous control on labworks

0.5 x note DS + 0.5 x note Compte rendu BE

Additional Information

Semester 9 - This course is given in english only 

Bibliography

Flandrin P.,
Temps Fréquences, Traité des nouvelles technologies, Série Traitement du Signal, Hermès, 1993

Chui C.K.,
An introduction to wavelets (Vol. 1), Wavelets - a Tutorial in theory and applications (Vol. 2), Wavelet analysis and its application, Academic Press, New York. 1992

Mars J, Mari J-L, Glangeaud F. et Lacoume J. L.,
Traitement du signal pour géologues et géophysiciens (Vol.3 - chap2). Editions Technip, 2005.