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)