Optimal and adaptive filters

Brief description

The course "Optimal and adaptive filters" introduces the basic techniques and theories of adaptive filtering. Based on the fundamentals of estimation theory, optimal filters are discussed first. The Wiener filter theory, deterministic optimisation under boundary conditions and stochastic gradient methods are then considered. Finally, the least squares approach to solving filter problems and the Kalman filter are presented. The latter can be seen as an introduction to the topic of state-based filtering.

Lecture contents

  • Classical parameter estimation: estimation and estimators, MMSE estimation, linear estimators, orthogonality principle, evaluation of the quality of estimators
  • Wiener filtering: Wiener-Hopf equation, AR and MA processes, linear prediction
  • Iterative optimisation methods: Gradient ascent/descent, Newton method
  • Linear adaptive filtering: LMS algorithm, least squares method, blockwise and recursive adaptive filters, realisation aspects
  • State model-based filters: Kalman filter
  • Applications: System identification, channel estimation and equalisation, multi-channel speech signal processing, noise and interference suppression

Results, competences & methodical implementation

After completing this course, students will be able to

  • analyse problems in the field of adaptive filtering and formulate requirements mathematically
  • develop filters based on cost functions and
  • implement selected adaptive filters in the frequency or time domain.

The students

  • are able to verify theoretical results in practical realisations,
  • can subject theoretical approaches to systematic analysis using a method-orientated approach and
  • are able to further their own education through the well-founded consideration of the contents.

Teaching methods

  • Lectures with the use of blackboards and presentations,
  • Alternating theoretical and practical face-to-face exercises with exercise sheets and computers and
  • Demonstrations of systems in the lecture


  • Course for Master students
  • ECTS: 6
  • Language: German, English (depending on students' wishes)
  • Semester: Winter semester


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Dr.-Ing. Jörg Schmalenströer

Communications Engineering / Heinz Nixdorf Institute

(Contract)-Research & Teaching

Write email +49 5251 60-3623


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Tobias Gburrek

Communications Engineering / Heinz Nixdorf Institute

Research & Teaching

Write email +49 5251 60-3624