Signal Processing

Lecture (2.0 VO)

This lecture course is built on the third semester course System Engineering and it covers discrete-time signals and systems, as well as signal processing algorithms:

  • Discrete-time signals in the time and frequency domains
  • Discrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)
  • z-transform
  • Sampling and signal reconstruction
  • Discrete-time systems in the time and frequency domains
  • Fast convolution
  • Multi-rate signal processing and sampling rate conversion
  • Spectral analysis and short-time Fourier transform
  • Digital filter design
  • Quantization effects due to signal conversion and finite arithmetic

The course notes as recorded during lecture presentation in previous years are available for downlaod in the TeachCenter (login required; link below).


In order to register for the exam follow a standard procedure at TUGraz online

The written exam consists of five short theoretical questions (20%) and four analytical problems (4*20%=80%). The duration is three hours. The copies of some previous exams are provided here to help you to prepare. You can download them here.

It is agreed that the following material is allowed during the exam:

  • A simple calculator. Alphanumerical calculators (such as TI-92, TI-89, TI Voyage and similar) are NOT allowed!
  • One mathematical formulary or handbook (e.g. Bartsch or Bronstein). Avoid to conceal any signal processing related examples inside your handbook.
  • A collection of signal processing formulas. This collection can be downloaded here (this is a new version; if you discover typos or mistakes, please contact Christian Knoll). Each student will be provided with this collection during the exam. You don't have to bring it with you.
  • Pencil, biro, pen, ... (different colors), ruler, etc., but NO PAPER! You will be provided with paper during the exam.
  • a drink, a small snack, ...

A remark on cheating: We advise you NOT to use any other material. Note that no jackets, no rucksacks, no bags, etc. are allowed in the vicinity of your desk during the exam. Cheaters wont be graded and wont be allowed to repeat the exam within 90 days ("Reprobationsfrist").

Problem Classes (1.0 UE)

The problem classes are arranged in 8 blocks of 90 minutes each and will be held on Mondays and Wednesdays. The classes start on 12th March 2018. The page and chapter numbers in the problem descriptions refer to the 3rd international edition of Oppenheim & Schafer, "Discrete-Time Signal Processing". 

No. Topic Material
1 Signals & Systems, Python Tutorial PDF
A word on notation,
2 Signals & Systems PDF
3 Signals & Systems II PDF

There are six different groups with five different time slots. See updated dates in TUG-Online!

Group Lecturer Room Time
1 Josef Kulmer HS i12 Monday, 09:00-10:30
2 Johannes Stahl HS i2 Monday, 10:30-12:00
3 Michael Rath HS i12 Monday, 10:30-12:00
4 Christian Toth HS i12 Monday, 16:15-17:45
5 Anna Fuchs HS i12 Wednesday, 17:15-18:45
6 Johannes Stahl IDEG134 Wednesday, 17:15-18:45



Homework Assignments

To pass the problem classes you have to prepare three homework assignments per semester, consisting of analytical and numeric software problems. The last assignment also consists of a Design Challenge, where the contestants can win some prizes. Last years' winners are devoted an additional webpage!

Assignments should be solved in groups of two students. Only one report needs to be delivered by each group. It is ok to work alone, although we do not recommend to do so (high work load). To make this point clear, work together with your group partner, and not with others.

it is allowed to exchange information with neighboring groups like 'take a look in Oppenheim/Schafer, Chapter 5', or 'we found something at Problem Class II'. It is not allowed to handle your solution to neighboring groups.


How to deliver your homework?

  • Deliver your homework online at teachcenter. 
  • Using LaTeX you may get additional 2 points per assignment. A template is available here. These additional points are considered ONLY if you have collected at least 50 points without them. 
  • Circumventing LaTeX is ok as long as we can read your handwriting; unreadability will cost several points.
  • Hand in Analytic solutions as a single .pdf document
  • Hand in numeric solutions as a single .pdf document plus the source code (either Python script (*.py) or Jupyther script (*.ipynb)). We strongly recommend to use Jupyther. It allows you to write your report along with your source code and thus, you save a lot of time.
  • Deliver each individual problem at teachcenter separately, e.g. hand in problems 1.1, 1.2 and 1.3 separately. This is required to ensure a fast grading.
  • For delivering your homework too late, you will lose 5 points/day.
  • In case not every problem assignment is delivered the missing ones are graded with zero points.
  • General guidelines (though written for Matlab they are valid for any kind of software).
  • What should be in your simulation protocol (numeric solutions)? Read this. (though written for Matlab, it is valid for Python as well)


Exploit the forum at teachcenter to exchange further information with us and your colleagues.

Time and place of the Q&A sessions (NOT for discussion of the grading!) will be announced in the forum!


For each assignment you can earn up to 34 points. You get at least 0 points for each assignment.

Achieved points
>= 89
76 <= ... < 89
63 <= ... < 76
50 <= ... < 63
< 50


References/Course Material


Problem Classes

  • A.V. Oppenheim, R.W. Schafer, J.R. Buck: Discrete-Time Signal Processing. Prentice-Hall, 1999 (2nd ed.). Strongly recommended! The course is based on this book (including the notation). You can buy the english version of the book here or lend it from the library.
  • Richard G. Lyons: Understanding Digital Signal Processing. Prentice-Hall, 2011 (3rd ed.). A quite pracitcal and intuitive introduction to DSP. There is an online version available on the TU Graz library's homepage.
  • Global JOS Index - An online ressourcre by Julius Orion Smith which covers a theoretical and practical signal processing topics.

Additional Literature for the Lecture

  • Richard A. Roberts and Clifford T. Mullis: Digital Signal Processing. Addison-Wesley, Reading (MA), 1987.
  • J.G. Proakis and D.G. Manolakis: Digital Signal Processing: Principles, Algorithms, and Applications. Prentice-Hall, 1995 (3rd ed.).
  • James H. McClellan, Ronald W. Schafer and Mark A. Yoder: DSP First: A Multimedia Approach. Prentice Hall, 1998.

Numeric software Python

  • We propose to use Jupyther as environment for Python, available at

 Additional Educational Ressources


Education Level: 
Bachelor Level