ADAPTIVE SIGNAL PROCESSING | ETT042 |

**Aim**

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.

*Knowledge and understanding*

For a passing grade the student must

- have knowledge about and understand the main concepts in 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

*Skills and abilities*

For a passing grade the student must

- be able to explain the main principles behind the most common 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 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.

**Contents***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

- 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

- Aspects when used
- Matlab implementation
- Numerical properties

**Literature**

Haykin S: Adaptive Filter Theory, Fourth Edition, Prentice-Hall 2001. Hardcover: ISBN 0-13-090126-1.