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.

Lecture (1.0 VO)

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

Part I is 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 Christoph Schörghuber (classes 1 to 4) and Bernhard Geiger (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.

  Problem Classes
 5  Fourier series
 6  Fourier series properties and trigonometric Fourier series
 7  Fourier transform properties
 8  Discrete time Fourier series


 Time and date of the exam will be announced in 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:

Date/Exam Solution
02.03.2012 Solution
27.04.2012 Solution
04.07.2012 Solution
12.10.2012 Solution
07.12.2012 Solution
25.01.2013 Solution
15.03.2013 Solution
26.04.2013 Solution
20.09.2013 Solution
14.03.2014 Solution
09.05.2014 Solution
30.01.2015 Solution
20.05.2016 Solution
17.03.2017 Solution
16.03.2018 Solution
04.05.2018 Solution
03.07.2018 Solution


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

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

Resources & Additional Material


  • 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.)


Education Level: 
Bachelor Level