Rima Alaifari: Catalogue data in Spring Semester 2021

Name Prof. Dr. Rima Alaifari
FieldApplied Mathematics
Seminar für Angewandte Mathematik
ETH Zürich, HG G 59.2
Rämistrasse 101
8092 Zürich
Telephone+41 44 632 32 00
RelationshipAssistant Professor

401-3426-21LTime-Frequency Analysis4 credits2GR. Alaifari
AbstractThis course gives a basic introduction to time-frequency analysis from the viewpoint of applied harmonic analysis.
ObjectiveBy 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.
ContentTime-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.
LiteratureGröchenig, K. (2001). Foundations of time-frequency analysis. Springer Science & Business Media.
Prerequisites / NoticeFunctional analysis, Fourier analysis, complex analysis, operator theory
401-5650-00LZurich Colloquium in Applied and Computational Mathematics Information 0 credits1KR. Abgrall, R. Alaifari, H. Ammari, R. Hiptmair, S. Mishra, S. Sauter, C. Schwab
AbstractResearch colloquium