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227-0101-00L 6 Credits BSC , MSC D-ITET , D-MATH

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Stochastic Models and Signal Processing

Stochastische Modelle und Signalverarbeitung

Lecturers & Examiners: Prof. Dr. Hans-Andrea Loeliger

VVZ CR 3.4

Last Updated: 2026-02-05 15:24:15

Abstract

The course introduces some fundamental topics of digital signal processing with a bias towards applications in communications: discrete-time linear filters, equalization, DFT, discrete-time stochastic processes, elements of detection theory and estimation theory, LMMSE estimation and LMMSE filtering, LMS algorithm, Viterbi algorithm.

Objective

The course introduces some fundamental topics of digital signal processing with a bias towards applications in communications. The two main themes are "linearity" and "probability". In the first part of the course, we deepen our understanding of discrete-time linear filters. In the second part of the course, we review the basics of probability theory and discrete-time stochastic processes. We then discuss some basic concepts of detection theory and estimation theory, as well as some practical methods including LMMSE estimation and LMMSE filtering, the LMS algorithm, and the Viterbi algorithm.

Content

Discrete-time linear systems and the z-transform. Discrete time and continuous time: forth and back. Digital filters. DFT. Elements of probability theory. Discrete-time stochastic processes. Elements of detection theory and estimation theory. Linear estimation and filtering. Wiener filter. LMS algorithm. Viterbi algorithm.

Resources

Lecture Notes

Lecture Notes.

General Information

Language: German
Levels: BSC , MSC
Frequency: Yearly recurring

Examination

Type: session examination
Mode: written 180 minutes
Aids: Vorlesungsskript, ein A4-Ordner mit beliebigen Notizen sowie Taschenrechner

Course Components

Type	Title	Time & Place	Hours
lecture with exercise	Stochastische Modelle und Signalverarbeitung	Tue 13:15-17:00 (ETF C 1)	4 h weekly

Offered In

Electrical Engineering and Information Technology Bachelor
- 5. Semester, Majors (Core Courses)
  - Communication
    - Compulsory Courses
  - Computer and Networking
    - Electives (These courses are recommended, but you are free to choose courses from any other major.)
  - Micro- and Optoelectronics
    - Compulsory Courses
    - Electives (These courses are recommended, but you are free to choose courses from any other major.)
  - Electrical Power Systems and Mechatronics
    - Electives (These courses are recommended, but you are free to choose courses from any other major.)
Mathematics Master
- Application Area (only necessary for the Master degree in Applied Mathematics)
  - Information and Communication Technology
Electrical Engineering and Information Technology Master
- Majors
  - Computer and Networking (A total of 42 CP must be achieved during the Master Program. The individual study plan is subject to the tutor's approval.)
    - Recommended Subjects (These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.)
  - Electrical Power Systems and Mechatronics (A total of 42 CP must be achieved during the Master Program. The individual study plan is subject to the tutor's approval.)
    - Recommended Subjects (These courses are recommended, but you are free to choose courses from any other special field. Please consult your tutor.)