## Statistical Signal Processing

Module Number: EI70240

Duration: 1 Semester

Occurence: Summer semester

Language: English

Number of ECTS: 5

## Staff

Professor in charge: Wolfgang Utschick

## Amount of work

Study hours: 90

Self-studying hours: 60

Total: 150

## Description of achievement and assessment methods

During a written examination without aids students prove that they are able to apply algorithms for statistical signal processing by answering questions and calculations.

**Exam type**: written

**Exam duration**: 90min.

**Possibilityof re-taking**: In the next semester: Yes At the end of the semester: No

**Homewor**k: No

**Lecture**: No

**Conversation:** No

**Written paper**: No

## Recommended requirements

Basic Classes in Probability Theory, Calculus, Linear Algebra, and Matrix Theory.

## Contents

Probability and stochastic processes: basic fundamentals revisited. Parameter estimation: statistical model, maximum likelihood estimation, Bayesian estimation, asymptotical optimality. Minimum mean squared error estimation: MMSE estimation, lineare MMSE estimation, orthogonality principle, Kalman filtering, Wiener filtering. Hypotheses testing: statistical model, Neyman-Pearson test, maximum-likelihood test, maximum a posteriori test, Bayesian test, risk functionals, sufficient statistics, asymptotical optimality, confidence analysis. Advanced topics: kernel approaches, partical filtering, etc.

## Study goals

At the end of the module, students are able to remember, understand and apply the theory, the basic methodologies and algorithms of statistical signal processing, and students are able to analyse, evaluate and create concepts, algorithms, and systems for the statistical estimation of deterministic and random parameters, variables, sequences and processes as they widely appear in information and communication systems and beyond.

## Teaching and learning methods

Learning method:

In addition to the individual methods of the students consolidated knowledge is aspired by repeated lessons in exercises and tutorials.

Teaching method:

During the lectures students are instructed in a teacher-centered style. The exercises are held in a student-centered way.

## Media formats

The following kinds of media are used:

- Presentations
- Lecture notes
- Exercises with solutions as download

## Literature

The following literature is recommended:

- A. Papoulis, S. Unnikrishna Pillai. Probability, Random Variables and Stochastic Processes, Mc Graw Hill
- Steven M. Kay. Statistical Signal Processing, Vol. I: Estimation Theory and Vol. II: Detection Theory, Prentice Hall Signal Processing Series
- Louis Scharf. Statistical Signal Processing, Prentice Hall
- Geoffrey R. Grimmett, David R. Stirzaker. Probability and Random Processes, Oxford University Press
- David J. C. MacKay. Information Theory, Inference, and Learning Algorithms, Cambridge University Press.