English
Mathematical and numerical aspects of frame theory - Part 1
Post-edited
Auteurs : Feichtinger, Hans G. (Auteur de la Conférence)
CIRM (Editeur )
15-XX - Linear and multilinear algebra; matrix theory
41-XX - Approximations and expansions [For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx]
42-XX - Harmonic analysis on Euclidean spaces
46-XX - Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]
CIRM (Editeur )
Résumé :
Motivated by the spectrogram (or short-time Fourier transform) basic principles of linear algebra are explained, preparing for the more general case of Gabor frames in time-frequency analysis. The importance of the singular value decomposition and the four spaces associated with a matrix is pointed out, and based on this the pseudo-inverse (leading later to the dual Gabor frame) and the Loewdin (symmetric) orthogonalization are explained.
CIRM - Chaire Jean-Morlet 2014 - Aix-Marseille Université
Codes MSC : CIRM - Chaire Jean-Morlet 2014 - Aix-Marseille Université
15-XX - Linear and multilinear algebra; matrix theory
41-XX - Approximations and expansions [For all approximation theory in the complex domain, see 30E05 and 30E10; for all trigonometric approximation and interpolation, see 42A10 and 42A15; for numerical approximation, see 65Dxx]
42-XX - Harmonic analysis on Euclidean spaces
46-XX - Functional analysis [For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx]
|
Informations sur la Vidéo
Réalisateur : Hennenfent, GuillaumeLangue : Anglais Date de publication : 06/11/14 Date de captation : 20/10/14 Sous collection : Research School arXiv category : Functional Analysis ; Mathematical Physics ; Numerical Analysis Domaine : Analysis and its Applications ; Mathematics in Science & Technology Format : QuickTime (.mov) Durée : 01:30:25 Audience : Researchers Download : https://videos.cirm-math.fr/2014-10-20_Feichtinger_part1.mp4 
|
Informations sur la Rencontre
Nom de la rencontre : Jean-Morlet Chair - Doctoral school: Computational harmonic analysis - with applications to signal and image processing / Chaire Jean-Morlet - Ecole doctorale : Analyse harmonique computationnelle - avec applications au traitement du signal et de l'imageOrganisateurs de la rencontre : Feichtinger, Hans G. ; Torrésani, Bruno ; Anthoine, Sandrine ; Chaux, Caroline ; Mélot, Clothilde Dates : 20/10/14 - 24/10/14 Année de la rencontre : 2014 URL Congrès : https://www.chairejeanmorlet.com/1250.html
Données de citation
DOI : 10.24350/CIRM.V.18613403Citer cette vidéo: Feichtinger, Hans G. (2014). Mathematical and numerical aspects of frame theory - Part 1. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18613403 URI : http://dx.doi.org/10.24350/CIRM.V.18613403 |
Bibliographie
Imagette Video
