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Mathematical and numerical aspects of frame theory - Part 1

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Post-edited
Authors : Feichtinger, Hans G. (Author of the conference)
CIRM (Publisher )

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spectrogram from STx program by ARI short-time Fourier transform GeoGebra biorthogonal system fast Fourier transform matrix multiplication null space of a matrix projection on the null space scalar product transpose matrix Gram matrix orthogonal projection rank of a matrix four subspaces row rank / column rank normal equation singular value decomposition pseudo inverse matrix polynomials on the unit circle Frobenius norm of a matrix Löwdin orthogonalization polar decomposition Vandermonde matrix Gauss function
Abstract : 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

MSC Codes :
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]
    Information on the Video

    Film maker : Hennenfent, Guillaume
    Language : English
    Available date : 06/11/14
    Conference Date : 20/10/14
    Subseries : Research School
    arXiv category : Functional Analysis ; Mathematical Physics ; Numerical Analysis
    Mathematical Area(s) : Analysis and its Applications ; Mathematics in Science & Technology
    Format : QuickTime (.mov) Video Time : 01:30:25
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2014-10-20_Feichtinger_part1.mp4
Information on the Event

Event Title : 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'image
Event Organizers : Feichtinger, Hans G. ; Torrésani, Bruno ; Anthoine, Sandrine ; Chaux, Caroline ; Mélot, Clothilde
Dates : 20/10/14 - 24/10/14
Event Year : 2014
Event URL : https://www.chairejeanmorlet.com/1250.html

Citation Data

DOI : 10.24350/CIRM.V.18613403
Cite this video as: 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

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