Learning outcomes

After a successfull completion of the course the student should be able to:

• design digital frequency selective filters according to practical limitations of a given problem,
• interpret and use the concepts of covariance matrices, auto-covariance, cross-covariance, wide-sense stationary processes and power density spectrum,
• design and implement optimal linear filters, such as Kalman and Wiener filters, and evaluate their applicability, optimality conditions and limitations for a given problem,
• design and implement parameter estimation methods, such as least-square (LS) solutions, and evaluate their limitations for a given problem,
• design and implement adaptive filters, with adaptation schemes such as LMS, RLS and evaluate their limitations for a given problem,
• implement some of the estimation methods introduced in the course using a numerical platform, such as MATLAB, and perform real-time or batch processing as appropriate.

Content

Digital frequency selective filters. Basic theory of stationary stochastic processes. Auto-covariance, cross-covariance. Power spectral density. Optimal linear estimation. Wiener filter. Kalman filter. Least mean square (LMS). Parameter estimation. Least-square estimation. Recursive least square (RLS).

Instruction

Lectures, guest lectures, assignments, tutorials and project supervision.

Assessment

Written exam at the end of the course (6 hp), oral and written presentation of assignments (2 hp), and oral and written presentation of project assignment (2 hp).