Adaptive Filters

In this course the fundamentals of adaptive filters are treated. Therefore, the necessary algorithms will be derived and demonstrated on examples from the field of speech and audio signal processing.


In summer semester 2022, this lecture will be offered as presence lecture. For more information, please register via TUCaN to get access to the moodle course.

Course Overview

Lecturer: Prof. Dr.-Ing. Henning Puder,
TU Darmstadt and Sivantos GmbH, Erlangen
Time: Lectures: Mondays, 8.00-10.30 a.m. (3 x 45 min + break)
4 Exercises: Mondays, 10.45-11.30 a.m. (1 x 45 min)
Start: Monday, April 11, 2022
Presence lecture: room S3|06 146

German or English on request; Lecture notes in English
Credit points:
6 credit points for Master students
Desirable prerequisites:
Basics in digital signal processing
Type of exam:
Oral. Prerequisites: Either you give a presentation on a selected “adaptive filter” topic. Or, you answer questions on a selected lecture. For details please check moodle.
The oral exam dates in summer term 2022 are planned to be offered in July and October, after and before the lecture period, respectively.

Part I – Basics

1. Introduction and application examples (part 1)

2. Signal models

3. Error criteria and cost functions

Part II – Algorithms

4. The Wiener filter
4.1 Fundamentals
4.2 Othogonality theorem
4.3 Extensions of the Wiener filter
4.4 Application examples

5. Linear prediction
5.1 Fundamentals
5.2 Normal equation
5.3 Rekursive calculation of the predictor coefficients
5.4 Application Examples

6. Algorithms for adaptive filters
6.1 The “Normalized Least Mean Square” (NLMS) algorithm
6.2 The filtered-x LMS algorithm
6.3 Methods of affine projection
6.4 The “Recursive Least Squares” (RLS) algorithm
6.5 Processing structures
6.6 Kalman filter
6.7 Properties and comparison of the algorithms

Part III – Acoustic echo and noise control

7. Fundamentals

8. Echo cancellation

9. Residual echo and noise suppression

10. Beamforming

11. Control of the algorithms and implementation issues

As exercise students can give talks. Each student can give a presentation. Details will be given in the lecture. A list of examples for possible topics for the talks as well as the dates of the talks can be found in the moodle course. A Microsoft PowerPoint template (voluntary) for the student talks is available for download below. A preliminary timetable for the student talks and topics will be provided via moodle.

Alternatively you can answer questions each week based on the previous lecture. In contrast to the talks you cannot get a bonus for the exam mark – only the admission..

  • E. Hänsler: Statistische Signale: Grundlagen und Anwendungen, Springer, 2001
  • E. Hänsler, G. Schmidt: Acoustic Echo and Noise Control, Wiley, 2004
  • S. Haykin: Adaptive Filter Theory, Prentice Hall, 2002#
  • A. Sayed: Fundamentals of Adaptive Filtering, Wiley, 2004
  • L. R. Rabiner, R. W. Schafer: Digital Processing of Speech Signals, Prentice Hall, 1978
  • P. Vary, U. Heute, W. Hess: Digitale Sprachsignalverarbeitung, Teubner, 1998
  • M. S. Hayes: Statistical Digital Signal Processing and Modeling, Signal Modeling, Wiley, 1996
  • J. R. Deller, J. H. l. Hansen, J. G. Proakis: Discrete-Time Processing of Speech Signals, Modeling Speech Production, IEEE Press, 2000
  • P. Vary, R. Martin: Digital Transmission of Speech Signals, Models of Speech Production and Hearing, Wiley 2006
  • R. Crochiere, L. Rabiner: Multirate Digital Signal Processing, Prentice Hall, 1983
  • K. D. Kammeyer, K. Kroschel: Digitale Signalverarbeitung, Teubner, 2002