Lecture "Adaptive Filters"


Basic Information
Lecturers: Gerhard Schmidt (lecture), Johannes Hoffmann and Karolin Kr├╝ger (exercise)
Room: Building F, room SR-I
Language: English
Target group: Students in electrical engineering and computer engineering
Prerequisites: Basics in system theory

Students attending this lecture should learn the basics of adaptive filters. To achieve this, necessary algorithms will be derived and applied to problems arising in speech and audio processing. The algorithms comprise Wiener filtering, linear prediction, and adaptive schemes such as the NLMS algorithm, affine projection, and the RLS algorithm. For applications from speech and audio processing we use noise and reverberation reduction, echo cancellation, and beamforming.

Topic overview:

  • Introduction and application examples
  • Signal properties and cost functions
  • Wiener filter and principle of orthogonality
  • Linear prediction
  • RLS algorithm
  • LMS algorithm and its normalized version
  • Affine projection algorithm
  • Control of adaptive filters
  • Efficient processing structures
  • Applications of linear prediction



16.05.2022: We moved the first student talk session from 18.05. to 25.05. Contact This email address is being protected from spambots. You need JavaScript enabled to view it. until 17.05. if you want to present on that date. Note that a talk is a prerequisite for admission to the exam. The earlier talk session was established due to students' demand to reduce stress during the busy examination period.



The following schedule regarding lectures and excercises is preliminary and may be adapted during the semester.

Each event starts at 8:15 h and might use the whole slot (lecture and exercise) until 11:45 h.

Date Event
13.04.2022 Lecture: Introduction
20.04.2022 Lecture: Wiener filter
27.05.2022 Lecture: Linear prediction
04.05.2022 Lecture: Algorithms part I
11.05.2022 Lecture: Algorithms part II
18.05.2022 Student talks I Lecture: Control
25.05.2022 Lecture: Control Student talks I
01.06.2022 Exercise: Question time and Python examples
08.06.2022 Lecture: Processing structures
15.06.2022 Lecture: Applications of linear prediction
22.06.2022 Exercise: Question time and Python examples
29.06.2022 Student talks II


Lecture Slides

Link Content
Slides of the lecture "Introduction"
(Introduction, boundary conditions of the lecture, applications)
Slides of the lecture "Wiener Filter"
(basics, principle of orthogonality, suppression of background noise)
Slides of the lecture "Linear Prediction"
(derivation of linear prediction, Levinson-Durbin recursion)
Slides of the lecture "Algorithms (Part 1 of 2)"
(RLS algorithm, LMS algorithm [part 1 of 2])
Slides of the lecture "Algorithms (Part 2 of 2)"
(LMS algorithm [part 2 of 2], affine projection algorithm)
Slides of the lecture "Control"
(basic aspect, pseudo-optimal control parameters)
Slides of the lecture "Processing Structures"
(polyphase filterbanks, prototype lowpass filter design)
Slides of the lecture "Applications of Linear Prediction"
(Improving the speed of convergence, filter design)



Link Content
Extension for the lecture "Wiener Filter"
(derivation of the error surface)


Matlab Demos

Link Content
Matlab demo (GUI based) for adaptive system identification
Matlab demo (GUI based) for adaptive noise suppression
Matlab demo (GUI based) for linear prediction
Matlab demo (GUI based) for the NLMS algorithms
Matlab demo (GUI based) for prediction-based filter design



There are two dedicated events with extended question time and python examples (cf., schedule). Apart from that, we provide on-demand videos and corresponding materials (e.g., questions and answers) for each topic below.

Exercises will be conducted according to the (preliminary) schedule above.

Video Content Material

Wiener filter:

  • summary
  • comprehension questions
  • python demo

Linear prediction:

  • summary
  • comprehension questions
  • signal visualization
  • python demo


  • summary
  • explaining algorithms
  • comprehension questions
  • python demo


  • motivation/summary
  • comprehension questions
  • python demo

Processing structures:

  • summary
  • comprehension questions
  • python demo


Student Talks

As part of the lecture, each student will give a talk about a certain topic as a prerequisite to sit the exam. The aim is both to give you the chance to work on an adaptive filter-related topic that interests you, and to improve your presentational skills. The talks should take ten minutes, plus 2.5 minutes of discussion and 2.5 minutes of feedback.

We offer two different presentation dates to choose from. Please contact This email address is being protected from spambots. You need JavaScript enabled to view it. with your topic suggestion and your prefered date. Below you can find the current schedule of the talks.


Date Room Time Topic Presenter(s)


Date Room Time Topic Presenter(s)



If you do not have a date for the exam yet please register in the online booking system (once the exam dates have been set). You can find the booking system here.


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