Aim
The course gives the basic knowledge in statistical signal processing and treats the theory and applications of optimal methods in filter design. The filter design methods are based on the statistical properties of the information signals as well as the additive noise.

Knowledge and understanding
For a passing grade the student must

• be able to apply optimal methods in signal modelling

• be able to apply optimal methods in processing signals in noisy environments

Skills and abilities
For a passing grade the student must

• have knowledge of problem formulations applied to signal modelling

• have knowledge of using statistical methods in estimation of signals in noise

Judgement and approach
For a passing grade the student must

• be able to read literature as well as treat with standards in this area

Contents
The following items are treated in the course: Matrices, random processes, spectral factorization. Signal modelling (IIR/FIR) using the Prony’ method. Normal equation and Levinson-Durbin recursive method, lattice filters. Estimation of reflection coefficients using Burgs algorithm. Optimal IIR and FIR filters (‘Wiener filters’), linear prediction, noise cancellation. Spectral estimation using non-parametric methods. Eigenvector methods in estimation of sinusoids in noise (Pisarenko, Music).

Applications: Filter for optimal noise cancellations are used in a wide area, i.e. mobile communication, acoustical signal processing, biomedical signals (EEG, ECG ). Spectral estimation has also a wide area of applications. Fast algorithms in signal processing are of great importance for VLSI design.

Literature
The literature mentioned was used last year. Hayes M: Statistical Digital Signal Processing and Modelling. John Wiley & Sons 1996. ISBN: 0471594318.