Course Syllabus for

# Optimum and Adaptive Signal Processing Optimal och adaptiv signalbehandling

## BMEN15F, 7.5 credits

Valid from: Autumn 2018
Decided by: Professor Thomas Johansson
Date of establishment: 2018-10-08

## General Information

Division: Biomedical Engineering
Course type: Course given jointly for second and third cycle
The course is also given at second-cycle level with course code: EITN60
Teaching language: English

## Aim

The course provides basic knowledge in statistical signal processing and the theory of optimal methods and how they can be applied. The course presents signal processing methodology and solutions to problems where digital systems tune in automatically and adapt to the environment. The student is given enough theoretical and practical knowledge to independently be able to formulate the mathematical problem, solve it and implement the solution for use with real-life signals.

## Goals

Knowledge and Understanding

For a passing grade the doctoral student must

• have knowledge about and understand the main concepts in optimum and adaptive filter theory
• be able to apply the most commonly used methods to real problems and real-life signals (Matlab-level)
• be able to formulate mathematical problems based on described situations

Competences and Skills

For a passing grade the doctoral student must

• be able to explain the main principles behind the most common adaptive methods (LMS and RLS)
• be able to explain/calculate the convergence and stability properties for these methods
• be able to sketch the most common block diagrams/structures used for adaptive filters and their properties
• be able to set parameters needed to make the algorithms work
• be able to foresee the consequences for the algorithms when implemented in fixed-point arithmetic
• be able to implement adaptive filters

Judgement and Approach

For a passing grade the doctoral student must

• have the ability to analyze, evaluate and implement adaptive algorithms, and be able to interpret and describe the principles which they are based on.
• have the insight that many different technical problems can be solved using the same methods.

## Course Contents

Optimum filtering -Wiener filters -Linear prediciton -The Levinson-Durbin algorithm Basics about adaptive filters -From optimal to adaptive filters -Cost functions, minimization problems and iterative procedures -Convergence and tracking capability, implementation aspects -Strategies for how to connect adaptive filters The LMS family -Principle and derivation -Convergence analysis and parameter settings -Variants including Normalized LMS, Leaky LMS, Fast LMS and Sign LMS -Matlab implementation -LMS in fixed-point arithmetic -Principle and derivation -Parameter settings The RLS family -Aspects when used -Matlab implementation -Numerical properties

## Course Literature

Haykin, S.: Adaptive Filter Theory. Pearson Education, 2014. ISBN 9780273764083.

## Instruction Details

Types of instruction: Lectures, laboratory exercises, exercises, project. Exercises 14 h, computer exercises 14 h and laboratory work 2 x 4 h

## Examination Details

Examination formats: Written exam, written report
Grading scale: Failed, pass
Examiner: