# EQ2401 Adaptive Signal Processing 7.5 credits

This course teaches adaptive signal processing algorithms for extracting information from noisy signals. The emphasis is on recursive, model based estimation methods for signals and systems whose properties change in time. Applications in, for example, communications, control and medicine are covered.

The course presents the fundamentals of adaptive signal processing; mean-square estimation, Wiener filters. Introduction to adaptive filter structures and the least squares method. State space models and optimal (Kalman) filtering. Stochastic gradient, LMS (least mean squares), and RLS (recursive least squares) methods. Analysis of adaptive algorithms: Learning curves, convergence, stability, excess mean square error, mis-adjustment. Extensions of LMS and RLS.

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Choose semester and course offering to see information from the correct course syllabus and course offering.

Headings with content from the Course syllabus EQ2401 (Spring 2019–) are denoted with an asterisk ( )

## Content and learning outcomes

### Course contents

This course teaches adaptive signal processing algorithms for extracting information from noisy signals. The emphasis is on recursive, model based estimation methods for signals and systems whose properties change in time. Applications in, for example, communications, control and medicine are covered.

The course presents the fundamentals of adaptive signal processing; mean-square estimation, Wiener filters. Introduction to adaptive filter structures and the least squares method. State space models and optimal (Kalman) filtering. Stochastic gradient, LMS (least mean squares), and RLS (recursive least squares) methods. Analysis of adaptive algorithms: Learning curves, convergence, stability, excess mean square error, mis-adjustment. Extensions of LMS and RLS.

### Intended learning outcomes

After completing the course, the student should be able to:

•                     Design and apply optimal minimum mean square estimators and in particular linear estimators. To understand and compute their expected performance and verify it.

•                     Design, implement and apply Wiener filters (FIR, non-causal, causal) and evaluate their performance.

•                     Design, implement and apply the different adaptive filters to given applications.

•                     Analyze the accuracy and determine advantages and disadvantages of each method.

•                     Use the theoretical understanding to do troubleshooting, e.g., in cases the observed performance is not as expected.

•                    Report the solution and results from the application of the filtering techniques to given problems.

### Course disposition

No information inserted

## Literature and preparations

### Specific prerequisites

For single course students: 180 ECTS credits and documented proficiency in English B or equivalent.

### Recommended prerequisites

Recommended prerequisites corresponding to: EQ1220 Signal theory or EQ1270 Signal processing

EQ2300 Digital Signal Processing

### Equipment

No information inserted

### Literature

Will be announced on the course homepage before course start.

## Examination and completion

If the course is discontinued, students may request to be examined during the following two academic years.

A, B, C, D, E, FX, F

### Examination

• PRO1 - Project 1, 1.5 credits, grading scale: P, F
• PRO2 - Project 2, 1.5 credits, grading scale: P, F
• TEN1 - Exam, 4.5 credits, grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

### Other requirements for final grade

2 Project assignments (PRO1, 1,5 ECTS credits, grading P/F; PRO2, 1,5 ECTS credits, grading P/F) completed and reported in pairs of at most 2 students before given deadlines.

Written exam (TENA, 4,5 ECTS credits, grading A-F)

### Opportunity to complete the requirements via supplementary examination

No information inserted

### Opportunity to raise an approved grade via renewed examination

No information inserted

### Ethical approach

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.

## Further information

### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web EQ2401

### Main field of study

Electrical Engineering

Second cycle