A Complete Framework for Linear Filtering of Bivariate Signals

Flamant, Julien; Chainais, Pierre; Le Bihan, Nicolas

Document type :

Article dans une revue scientifique: Article original

DOI :

10.1109/TSP.2018.2855659

Title :

A Complete Framework for Linear Filtering of Bivariate Signals

Author(s) :

Flamant, Julien [Auteur]
Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 [CRIStAL]
Chainais, Pierre [Auteur]

Laboratoire d'Informatique, de Modélisation et d'optimisation des Systèmes [LIMOS]
Le Bihan, Nicolas [Auteur]
GIPSA - Communication Information and Complex Systems [GIPSA-CICS]

Journal title :

IEEE Transactions on Signal Processing

Pages :

4541-4552

Publisher :

Institute of Electrical and Electronics Engineers

Publication date :

2018-09-01

ISSN :

1053-587X

HAL domain(s) :

Sciences de l'ingénieur [physics]/Traitement du signal et de l'image [eess.SP]

English abstract : [en]

A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms ...
Show more >A complete framework for the linear time-invariant (LTI) filtering theory of bivariate signals is proposed based on tailored quaternion Fourier transform. This framework features a direct description of LTI filters in terms of their eigenproperties enabling compact calculus and physically interpretable filtering relations in the frequency domain. The design of filters exhibiting fundamental properties of polarization optics (birefringence and diattenuation) is straightforward. It yields an efficient spectral synthesis method and new insights on Wiener filtering for bivariate signals with prescribed frequency-dependent polarization properties. This generic framework facilitates original descriptions of bivariate signals in two components with specific geometric or statistical properties. Numerical experiments support our theoretical analysis and illustrate the relevance of the approach on synthetic data.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :