Skip to Main content Skip to Navigation
New interface
Theses

Une approche générique pour l'analyse et le filtrage des signaux bivariés

Abstract : Bivariate signals appear in a broad range of applications (optics, seismology, oceanography, EEG, etc.) where the joint analysis of two real-valued signals is required. Simple bivariate signals take the form of an ellipse, whose properties (size, shape, orientation) may evolve with time. This geometric feature of bivariate signals has a natural physical interpretation called polarization. This notion is fundamental to the analysis and understanding of bivariate signals. However, existing approaches do not provide straightforward descriptions of bivariate signals or filtering operations in terms of polarization or ellipse properties. To this purpose, this thesis introduces a new and generic approach for the analysis and filtering of bivariate signals. It essentially relies on two key ingredients: (i) the natural embedding of bivariate signals -- viewed as complex-valued signals -- into the set of quaternions H and (ii) the definition of a dedicated quaternion Fourier transform to enable a meaningful spectral representation of bivariate signals. The proposed approach features the definition of standard signal processing quantities such as spectral densities, linear time-invariant filters or spectrograms that are directly interpretable in terms of polarization attributes. More importantly, the framework does not sacrifice any mathematical guarantee and the newly introduced tools admit computationally fast implementations. Numerical experiments support throughout our theoretical developments. We also demonstrate the potential of the approach for the nonparametric characterization of the polarization of gravitational waves.
Document type :
Theses
Complete list of metadata

Cited literature [226 references]  Display  Hide  Download

https://theses.hal.science/tel-01926941
Contributor : ABES STAR :  Contact
Submitted on : Monday, November 19, 2018 - 3:14:07 PM
Last modification on : Tuesday, November 22, 2022 - 2:26:16 PM
Long-term archiving on: : Wednesday, February 20, 2019 - 3:15:43 PM

File

Flamant_Julien_DLE.pdf
Version validated by the jury (STAR)

Identifiers

  • HAL Id : tel-01926941, version 1

Collections

Citation

Julien Flamant. Une approche générique pour l'analyse et le filtrage des signaux bivariés. Traitement du signal et de l'image [eess.SP]. Ecole Centrale de Lille, 2018. Français. ⟨NNT : 2018ECLI0008⟩. ⟨tel-01926941⟩

Share

Metrics

Record views

476

Files downloads

299