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401-3426-21L 4 Credits BSC , MSC D-MATH
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Time-Frequency Analysis

Lecturers & Examiners: Dr. Rima Alaifari
VVZ CR n/a

Last Updated: 2026-02-05 15:54:09

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 , MSC

Examination

Type
session examination
Mode
oral 20 minutes
Four sessions of the semester (11.3., 1.4., 6.5., 3.6.) will be held as an exercise class. The active participation in these exercise classes via submission of solutions and presentations as a voluntary learning task will be graded and can improve the total course unit grade by up to 0.25 grade points. Students can still achieve the maximum grade of 6 in the course unit even if they only take the final examination.

Course Components

Type Title Time & Place Hours
lecture with exercise Time-Frequency Analysis
For more details concerning this online course see
  • Thu 12:15-14:00 (HG F 26.5)
2 h weekly

Offered In