Optimal and adaptive filters

Brief description

Calculation of a filter coefficient in the adaptive filter

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