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250130 VO Gabor Analysis: From Linear Algebra to Computational Harmonic Analysis (2021W)

3.00 ECTS (2.00 SWS), SPL 25 - Mathematik
MIXED

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes

Currently no class schedule is known.

Information

Aims, contents and method of the course

The goal of the course it to provide a link between basic linear algebra and Gabor analysis. In a musical context (cf. MP3) this means, that one computes locally (with the help of the FFT, the Fast Fourier transform) the frequency content. This is like musical score computed digitally from the recording.
The goal of the course is to provide the a link between the introductory courses and the world of time-frequency analysis, with a computational component.
The course material will be developed as the course goes, in parallel with already existing (huge amounts) of material within the work group NuHAG (Numerical Harmonic Analysis Group, with K.Gröchenig, P.Grohs, M.Dörfler, M.Ehler, P.Balazs, M.Faulhuber, etc.).
The computational part will be based on MATLAB, a mathematical software (MATrix LABoratory, i.e. linear algebra as software package), but no previous programming or MATLAB experience will be required.

Existing comprehensive collections of MATLAB routines will be provided by the lecturer.

Material for an earlier course plus YouTube links (ETH Zuerich, Autumn 2020) are found at
www.nuhag.eu/ETH20

Assessment and permitted materials

There are two components:
1) oral examination on the foundations and background of Gabor analysis and time-frequency analysis in the finite dimensional setting
2) either written reports on a circle of problems, or a collection of M-files (a small, self-contained demonstration package), complementary to the routines made available.

The so-called Life-Script for MATLAB is the ideal way to provide both (running MATLAB code plus LATEX output, including figures and so on).

Minimum requirements and assessment criteria

In order to pass the candidates have to demonstrate that they have understood the basic principles of the course, meaning the foundations coming from linear algebra (e.g. pseudo-inverse of a matrix, symmetric orthogonalization based on the SVD, and so on) and the (mostly algebraic) rules governing Gabor analysis, which are also the basis for the most efficient algorithms.

Examination topics

The concrete list of questions will be provided during the course. There will be course notes and the material required to pass will be summarized. As it is a complementary course it will be possible to individually adapt the material (for example, the course could be interesting to new-comers to the field, or those who have already taken the course with Markus Faulhuber last semester, or taking the parallel course with Peter Balazs on FRAMES this semester).

Reading list

There will be a large amount of material available to the students. Access to the repositoy
www.nuhag.eu/bibtex
will be provided by the lecturer (ask for access code).
see also www.nuhag.eu/talks (access via "visitor" and "nuhagtalks", autor : Feichtinger)
several books are available in the NuHAG library, e.g.
Karlheinz Gröchenig [gr01]
Foundations of Time-Frequency Analysis
Birkhäuser, Appl. Numer. Harmon. Anal., (2001)

Association in the course directory

MAMV; MANV

Last modified: Su 19.09.2021 11:08