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250087 VO Frame Theory (2021W)
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Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Friday
04.02.2022
Friday
25.02.2022
Tuesday
29.03.2022
Friday
22.04.2022
Friday
01.07.2022
Tuesday
31.01.2023
Lecturers
Classes (iCal) - next class is marked with N
Tuesday
05.10.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
07.10.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
12.10.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
14.10.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
19.10.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
21.10.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Thursday
28.10.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Thursday
04.11.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
09.11.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
11.11.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
16.11.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
18.11.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
23.11.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
25.11.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
30.11.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
02.12.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
07.12.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
09.12.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
14.12.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
16.12.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
11.01.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
13.01.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
18.01.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
20.01.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Tuesday
25.01.
11:30 - 12:15
Seminarraum 14 Oskar-Morgenstern-Platz 1 2.Stock
Thursday
27.01.
13:15 - 14:45
Seminarraum 16 Oskar-Morgenstern-Platz 1 3.Stock
Information
Aims, contents and method of the course
Assessment and permitted materials
Written exam(In exceptional cases an oral exam is possible.)
Minimum requirements and assessment criteria
A basic understanding of concepts from functional analysis and linear algebra.For a successful conclusion of this course, students must demonstrate knowledge of the basic concepts and theorems, as well as an understanding of the main proofs and applications presented.
Examination topics
Everything that is covered in the course, i.e.
1.) Spanning sets in finite dimensional vector spaces
2.) Bessel sequences
3.) Riesz bases
4.) Frames
5.) Particular frame systems: Gabor, Wavelets, Shift-invariant Systems
1.) Spanning sets in finite dimensional vector spaces
2.) Bessel sequences
3.) Riesz bases
4.) Frames
5.) Particular frame systems: Gabor, Wavelets, Shift-invariant Systems
Reading list
The course will mostly stick to
Ole Christensen, An Introduction to Frames and Riesz Bases
Ole Christensen, An Introduction to Frames and Riesz Bases
Association in the course directory
MANV; MAMV
Last modified: We 01.02.2023 00:26
(i) recovered from its frame coefficients, i.e. the inner products with respect to the frame elements and
(ii) expanded into a linear combination of the frame elements.
Frames have a rich structure despite being much less restrictive than ONBs, rendering them attractive for a wide number of applications. In addition to being an active field of research, posing interesting research questions of its own, frame theory has applications in other fields, like signal processing and physics.Students of this course will gain understanding of the basic properties of frames and Riesz bases in comparison to ONBs, both in a linear algebra and functional anaylsis context. Particular The implementation of frame-related algorithms will be considered and applications in acoustics, signal processing and quantum mechanics are presented as motivation.For a short introduction see
https://en.wikipedia.org/wiki/Frame_(linear_algebra)This will be a standard frontal course, using mostly the blackboard and ocaasionally the beamer.