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Optimal and adaptive Filter

Adaptive filter coefficient calculation

Short Description

The course “Optimal and adaptive filters” gives an introduction to the basic techniques and theories of adaptive filters. Based upon the basics of estimation theory optimal filters are discussed. Subsequently the topics Wiener filter theory, deterministic optimization under constraints and stochastic gradient methods are regarded. Concluding the Least Squares approach for solving filter tasks and the Kalman filter are introduced. The latter is regarded as a brief introduction to state based filters.


  • Classic parameter estimation: Estimators, MMSE-Estimation, Linear estimators, Orthogonality principle, Evaluation of estimators
  • Wiener filter: Wiener-Hopf equation, AR- and MA processes, Linear predictionIterative optimization methods: Gradient ascent/descent, Newton method
  • Linear adaptive filters: LMS algorithm, Least-Squares method, Blockwise and recursive adaptiv filters, Realization aspects
  • Statemodel based filters: Kalman filter
  • Applications: System identification, Channel estimation and equalization, Multi-channel speech signal processing, Noise and interference suppression

    Learning Outcomes, Competences & Implementation

    After attending the course, the students will be able to

    • analyze task on the field of adaptive filters and to formulate requirements mathematically,
    • develop filter using cost functions and
    • implement selected adaptive filters in the frequency or time domain.

    The students

    • are able to check theoretical results using practical realizations,
    • are able to undertake theoretical approaches a systematic analysis using methodical procedures and
    • are, due to the precise treatment of the contents, in a position to continue their learning themselves.


    • Lectures using the blackboard and presentations,
    • Alternating theoretical and practical exercises classes with exercise sheets and computer and
    • Demonstration of real technical systems in the lecture hall.

    General Information

    • Course for Master Students
    • ECTS: 6
    • Language: German or English (depending on preference of students)
    • Semester: Wintersemester

    The University for the Information Society