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401-3426-21L 4 Credits BSC , DR , MSC D-ITET , D-MATH

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Time-Frequency Analysis

Lecturers & Examiners: Dr. Rima Alaifari

VVZ CR n/a

Last Updated: 2026-02-05 16:14:48

Abstract

This course gives a basic introduction to time-frequency analysis from the viewpoint of applied harmonic analysis.

Objective

By the end of the course students should be familiar with the concept of the short-time Fourier transform, the Bargmann transform, quadratic time-frequency representations (ambiguity function and Wigner distribution), Gabor frames and modulation spaces. The connection and comparison to time-scale representations will also be subject of this course.

Content

Time-frequency analysis lies at the heart of many applications in signal processing and aims at capturing time and frequency information simultaneously (as opposed to the classical Fourier transform). This course gives a basic introduction that starts with studying the short-time Fourier transform and the special role of the Gauss window. We will visit quadratic representations and then focus on discrete time-frequency representations, where Gabor frames will be introduced. Later, we aim at a more quantitative analysis of time-frequency information through modulation spaces. At the end, we touch on wavelets (time-scale representation) as a counterpart to the short-time Fourier transform.

Resources

Literature

Gröchenig, K. (2001). Foundations of time-frequency analysis. Springer Science & Business Media.

General Information

Language: English
Levels: BSC , DR , MSC

Examination

Type: session examination
Mode: oral 20 minutes

The exam is only offered in the two examination sessions immediately following the course, that is, Winter 2024 and Summer 2024.

Course Components

Type	Title	Time & Place	Hours
lecture	Time-Frequency Analysis	Tue 10:15-12:00 (ML J 34.1)	2 h weekly

Offered In

Mathematics Bachelor
- Electives
  - Selection: Numerical Analysis
Mathematics Master
- Electives (For the Master's degree in Applied Mathematics the following additional condition (not manifest in myStudies) must be obeyed: At least 14 of the required 26 credits from core courses and electives must be acquired in areas of applied mathematics and further application-oriented fields.)
  - Electives: Applied Mathematics and Further Application-Oriented Fields (¬)
    - Selection: Numerical Analysis
Electrical Engineering and Information Technology Master
- Master Studies (Programme Regulations 2018)
  - Track: Signal Processing and Machine Learning (The core courses and specialisation courses below are a selection for students who wish to specialise in the area of "Signal Processing and Machine Learning ", see . The individual study plan is subject to the tutor's approval.)
    - Specialisation Courses (These specialisation courses are particularly recommended for the area of "Signal Processing and Machine Learning", but you are free to choose courses from any other field in agreement with your tutor. A minimum of 40 credits must be obtained from specialisation courses during the MSc EEIT.)
- Master Studies (Programme Regulations 2008)
  - Major Courses (A total of 42 CP must be achieved during the Master Programme. The individual study plan is subject to the tutor's approval.)
    - Signal Processing and Machine Learning
      - Recommended Subjects
Doctorate Information Technology and Electrical Engineering (More Information at: )
- Subject Specialisation (A minimum of 12 ECTS credit points must be obtained during doctoral studies. The courses on offer below are only a small selection out of a much larger available number of courses. Please discuss your course selection with your PhD supervisor.)