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Ihre Position


Multirate Signal Processing

Lehrverantwortlicher: Prof. Dr.-Ing. Gerald Schuller


  • Sampling in one and more dimensions (Images...)
  • z-Transforms in multirate systems
  • Filter banks for coding applications
  • Polyphase representation
  • Low Delay Filter banks
  • Integer Filterbanks
  • Prediction
  • Application examples

Teaching documents

Lecture 1: Intro
Lecture 2: Spectrogram, DTFT, DFT, z-Transform [pdf]
Lecture 3: Frequency domain, Frequency response, Filtering, Decibel[pdf]
Lecture 4: Filters[pdf]
Lecture 5: Filters, Windows[pdf]
Lecture 6: Windows, Sampling[pdf]
Lecture 7: Sampling[pdf]
Lecture 8: z-Domain effects[pdf]
Lecture 9: non-ideal filters[pdf]
Lecture 10: Transforms as Filter Banks[pdf]
Lecture 11: DCT, Polyphase Description[pdf]
Lecture 12: Polyphase Representation[pdf]
Lecture 13: MDCT[pdf]
Lecture 14: Low Delay Filter Banks[pdf]
Lecture 15: Optimization[pdf]
Lecture 16: Neural Networks[pdf]
28. April 2016: Homework 1
04. May 2016: Homework 2 PDF
24. May 2016: Homework 3PDF
08. June 2016: Homework 4PDF
21. June 2016: Homework 5PDF



Python examplesDownload


Additional Information:

  • Python programs for the lectures, together with python notebook files: Examples


Installation of Python:

For the installation of Python in Windows, Mac or Ubuntu Linux you can find a description in It is easiest for Ubuntu Linux (just one click in the Ubuntu Software Center).


For Windows:

Go to Download PythonXXX.exe and execute it for installation. For our course you need extra Python libraries (e.g. numpy, scipy, matplotlib, etc.). In order to install extra libraries you can use pip installer program. You can find more full description of pip usage here

One more way to install full Python with all basic libraries in Windows is to install Python(x,y). Python(x,y) is a free scientific and engineering development software for numerical computations, data analysis and data visualization based on Python programming language, Qt graphical user interfaces and Spyder interactive scientific development environment. Full description of Python(x,y) and installation file can be found here


For Ubuntu:

Ubuntu comes with pre-installed Python. However, extra libraries have to be installed separately. It can be done using pip installer. 

To install something in Ubuntu command sudo apt-get install pkg_name can be used. 


- to install pip installer:

sudo apt-get install python-pip

 - to install numpy, scipy and matplotlib using pip:

sudo pip install numpy scipy matplotlib

- to install numpy, scipy and matplotlib using apt-get:

sudo apt-get install python-numpy python-scipy python-matplotlib


The Python Tutorial can be found here or use google and Stackoverflow.

Summer Semester 2020

First Online Lecture: 22-nd April 2020

First Seminar: 30-th April 2020

Due to the quarantine the actual dates are subject to change!!!


Every new Lecture and seminar will be announced thru Moodle Forum. How Seminars will tough in the current semester is still not known, most probably also online. For this, you have to be enrolled for this course in Moodle2 system.

Lectures 2020:

Given by: Prof. Dr.-Ing. Schuller

Wednesday09:00 - 10:30Sr HU 010


Practice Lessons 2020:

Given by: M.Sc. Oleg Golokolenko

Thursday (even weeks)09:00 - 10:30H 1520a


Please, register in Moodle2 to download up to date lecture slides and seminar documents. You can use the forums in Moodle to ask questions or as a simple communication platform.



Exams (written)



There will be periodic homework assignments, which will count 30% towards the final grade.

You may form small groups (2-3 people) to solve the homework and deliver a single solution for the whole group. Please present your homework in a digital form (e.g. source code on a flash storage device or laptop with Python.)

In addition there will be assignments on Moodle, which count 25% towards the homework..

Homework assignments may take about 6-8 hours per week to solve per 2 week cycle.

Literature and Links


G. Strang, T. Nguyen,  "Wavelets and Filter Banks", Wellesley College, 1996
N. J. Fliege, "Multirate Digital Signal Processing", John Wiley & Sons Ltd., 1993
N. Fliege, "Multiraten-Signalverarbeitung: Theorie und Anwendungen", Teubner, Stuttgart, 1993