This lecture course is designed for the second-semester students and it covers basics of the Fourier analysis for discrete-time and continuous-time signals, as well as Laplace- and Z-Transforms.

TU Graz TeachCenter

The current information about this course can be found in the TU Graz TeachCenter.

Lecture (1.0 VO)

The material covered by this course is split into two parts:

Part Iis taught by Prof. Nicolaos Dourdoumas from the Institut für Regelungs- und Automatisierungstechnik, and includes:

• Laplace-transform
• Z-transform

Part II is given by Prof. Klaus Witrisal from the SPSC Laboratory (Institut für Signalverarbeitung and Sprachkommunikation). Part II covers the following topics:

• Fourier series for periodic continuous-time signals
• Fourier series for periodic discrete-time signals
• Fourier transform for aperiodic continuous-time signals
• Fourier transform aperiodic discrete-time signals

An overview of these topics can be found in the slide set used in the lecture course. (Course slides)

Problem Classes (1.0 UE)

The lecture course is also accompanied by the problem classes that cover the computational aspects of the theoretical part of the course. The main accent is placed on demonstrating analytical techniques for computing the Fourier-, Laplace-, and Z-transforms on easy-to-follow examples.

In addition to the examples calculated during the lecture, additional problem classes will be held by Stefan Lambert Hölzl (classes 1 to 4) and Julian Linke (classes 5 to 8). Although the participation in these additional classes is not mandatory, they demonstrate a set of possible computational problems that one will encounter during the examination. They also should help you to better understand the course material.

The assignment sheets for the problems to be solved in the additional problem classes can be found in the table below. Whenever a (sub-)task is followed by a star, this indicates that the corresponding problem may be a bit too difficult (or too long) for an exam problem.

Exam

Time and date of the exam will be announced in TUGraz.online. Please note that formularies, pocket calculators, or other supporting material are not allowed!In order to help you prepare for the coming exams, we provide copies of previous exams along with some solutions:

Newsgroup

There will also be a newsgroup available for the exchange of information and questioning concerning both lecture course and problem classes. The newsgroup address is tu-graz.lv.signaltransformationen.

The threads from the previous year(s) can be found in the archive.

Resources & Additional Material

• Illustration of truncated Fourier series expansions and Gibbs phenomenon
• Table of Fourier transform and Fourier series properties
• Trigonometric identities
• Table of commonly used integrals

References

• A.V. Oppenheim, A.S. Willsky, S.H. Nawab: Signals and Systems. Prentice-Hall, 1996 (2nd ed.)
• Athanasios Papoulis: Circuits and Systems. Oxford University Press, 1979.
• Otto Foellinger: Laplace-, Fourier- und z-Transformation. Huethig, 2003 (8th ed.)