Time-frequency analysis of noisy multicomponent signals: contributions to ridge detection, mode reconstruction, chirp rate estimation, and interference localization.

Keywords :

• signaux multicomposantes
• débruitage

Time-frequency analysis is commonly used to study real world signals. These can often be described as multicomponent signals made of the sum of frequency and amplitude modulated modes. This thesis describes time-frequency techniques to study such signals in heavy noise situations, by dealing with three major issues. The first one is to design robust ridge detection technique and linear chirp approximation to improve instantaneous frequency estimation and mode reconstruction. The results demonstrate that an accurate ridge detection is a necessary but not a sufficient condition to ensure an accurate mode reconstruction. The second issue is the identification and the separation of interfering modes. To address this issue, the approach we propose focuses on ridge detection to localize patterns, coined time frequency bubbles, associated with interference in the time-frequency plane. The third issue is on the adaption of the synchrosqueezing transform to the frequency modulation of the modes and to noise. Regarding the first aspect, an energy based criteria is defined to measure the concentration of a time-frequency representation, which we use to adapt the synchrosqueezing technique. On the noise issue, based on a theoretical study of the effect of noise on the chirp rate estimator used in synchrosqueezing transforms, a new chirp rate denoising technique is proposed improving the estimation. The fourth and last issue is the heart rate estimation on ECG signals using time-frequency analysis, for which we design a specific algorithm. We show that the choice of the representation has huge consequences and demonstrate that it should be taken into account.

President:

DR Patrick Flandrin (CNRS DELEGATION RHONE AUVERGNE)

Directors:

• MdC HDR Sylvain Meignen (GRENOBLE INP )
• MdC HDR Bertrand Rivet (GRENOBLE INP )
• MdC Julie Fontecave-Jallon (Université Grenoble Alpes )

Raporteurs:

• Professeur Maria Sandsten (Lund Universitet )
• Professeur Roland Badeau (Telecom Paris )

Examinators:

• Professeur Jérôme Mars (GRENOBLE INP )
• Professeur Pierre Chainais (ECOLE CENTRALE LILLE )