Feb. 1: Tutorials and Exam Questions - Update
Dear Students, please find here the links to the slides of last Monday's tutorial. Furthermore, please download the questions to be discussed during the oral examinations. Have a nice and please excuse the...[more]
Jan 27:
Dear Students of TVSC, please find slides for the topics on Inner-Outer Factorization and on Kalman Filtering, which I will use in tomorrow's lecture. The slides are thanks to Patrick Dewilde, who is kind enough to share his...[more]
Jan. 11 - Numerical Example
Please find here an elaborate Numerical example “Numex.pdf” for the homework assignment 3. The matrices used for generating this example can be found in the “numex.mat” file. If you wish to use the constructSSS...[more]
Jan 2: Homework #3
Dear Students, we wish you all a Happy New Year. Please find here the description of Homework #3 along with a set of accompanying Matlab files. Same procedure as last year ... CU soon kldi & Sunil[more]
Dec. 21:
Dear students, please find here the slides for the material presented last Monday in class. Note that we will upload an updated version of those slides shortly, where we adjust the nomenclature of the mathematics to be in line...[more]
Dec. 10: Pecha Kucha Slides
Even though I have missed to give a Pecha Kucha presentation in class today, I upload my pecha kucha slides for a presentation on Georg Simon Ohm. I hope I can present it some other time. [more]
Dec. 9: Write up for lecture 7
Please find here the write up for lecture 7. If you want to access more details on how to actually compute the eigenvalue decomposition (EVD) or the singular value decomposition (SVD) I recommend to have a...[more]
| Dozent: | Klaus Diepold |
| Assistenten: | Sunil Tatavarty |
| Zielgruppe: | Students in MSCE and MSEI |
| ECTS: | 6 Credits |
| Umfang: | 3 SWS |
| Turnus: | Wintersemester |
| Anmeldung: | no registration necessary |
| Zeit & Ort: | Z995 |
| Beginn: | October 15, 2012 |
Target Audience
Compulsory elective course for MSCE (1st / 3rd semester). Elective course for EI (semester 7 and higher) students (Diplom and MSEI).
Registration and Prerequisites
- No registration necessary
- Working knowledge of state space description for linear time invariant (LTI) systems
- Working knowledge of Linear Algebra and Matlab.
ECTS Information
3 SWS, 6 ECTS Credits, MSCE, MScEI
3 SWS, 4.5 ECTS Credits, Diplom EI, SIM
Time and Venue
Mondays 11:30 - 14:00 (inkl. breaks), Z995, starting on Monday, 15.10.2012
Contents
A broad range of engineering problems involve the solution of large systems of linear equation or other linear algebra computations involving large matrices. This includes finding the best search result using Google’s “PageRank” technology to designing large-scale integrated semiconductor circuits. Other signal processing tasks can also be represented in this way. We mostly assume the linear systems to be time-invariant. This assumption enables us to use traditional tools in system modeling such as computing the response of a system in the frequency-domain (using FFTs) or using the z-transform.
However, there are systems where the property of time-invariance is not satisfied and where frequency-domain operations are no longer feasible. The purpose of this course is to introduce an alternative way to treat linear systems that generalizes also to time-varying systems. Linear Systems will be described in terms of a state-space realisation, which uses concepts of linear algebra and Hilbert Space tools. The course emphasizes the representation of large-scale computational problems (matrix-vector mulitplication, matrix inversion, matrix factorization, etc.) as problems of time-varying linear systems. This approach allows that engineers can apply linear system based thinking to design fast and efficient numerical algorithms for large-scale linear algebra problems.
The exercise focuses on revision of fundamental mathematical concepts like vector spaces, linear algebra, matrix factorizations (Polar Decomposition, Cholesky Decomposition, Singular Value Decomposition, Eigenvalue Decomposition etc.) along with the extension of representing linear time invariant systems to time-varying systems. Of course, a few engineering applications will also be discussed (modelling VLSI circuits, matrix inversion, matrix approximation, W-CDMA Rake receivers, non-causal prediction of image coding, etc.). The course includes some projects where Matlab programs will be developed to implement algorithms.
Outline:
- Review of time-invariant systems and signals
- Large scale computations in engineering and science
- State-space representation of LTV systems
- Realization theory for LTV systems
- The Exercise will focus to provide the necessary mathematical background for the course
- For details contact...
Reference Literature:
- P.Dewilde, A.-J. van der Veen. Time-Varying Systems and Computations. Kluwer Academic Publishers, 1998.
The background mathematical knowledge (also covered in exercise) is available in:
- G. Strang. Linear Algebra and its Applications. Hartcourt Brace Jovanovich Publishers, San Diego, 1988.
Grade Structure
Final Examination (Oral) 50%; Homework and Projects 50%.
