January 24, 2019

Gabor analysis is a part of time-frequency analysis concerned with localized Fourier expansions of a given signal. In the one-dimensional case, it corresponds to the Fourier analysis of segments of an audio signal via the discrete/fast Fourier transform (DFT/FFT).

Gabor analysis is a part of time-frequency analysis concerned with localized Fourier expansions of a given signal. In the one-dimensional case, it corresponds to the Fourier analysis of segments of an audio signal via the discrete/fast Fourier transform (DFT/FFT). It can be viewed as a kind of inversion of the process of producing music from a score. Sometimes the pictures obtained by this transform, spectrograms, look like a graphical composition. The method is also the basis for the MP3 compression algorithm for audio data. In two dimensions one can compare the approach with JPEG image compression. But instead of a decomposing an image into disjoint 8x8 blocks, one has overlapping blocks with smooth transitions.

While the foundations of this theory go back to a paper by D. Gabor from 1946, the mathematical analysis and parallel to it its computational realization have started only in the late 80s of the last century. The talk will illustrate the applications and describe how mathematical analysis including the speaker’s own results has helped to overcome the computational questions involved in this problem. The demonstration at www.gaborator.com provides a convincing illustration of the subject using audio signals.

Professor Hans Georg Feichtinger spent most of his career at the University of Vienna, where he also received his PhD in 1974. His main interests are harmonic analysis with particular focus on time-frequency analysis and Gabor analysis, from the theoretical, applied as well as the computational side. H. G. Feichtinger is the founder of the Numerical Harmonic Analysis Group (NuHAG) in Vienna, which under his leadership received eight Marie Curie Fellowships and one Marie Curie Excellence Grant. He supervised 31 PhD students, several of them currently holding positions at ETH Zürich, DTU Copenhagen, TU München, and RWTH Aachen. He is an Editor in Chief of the Journal of Fourier Analysis and Applications since 2000. He has held visiting positions at Heidelberg University, Univ. of Maryland at College Park, Univ. of Connecticut at Storrs, Univ. of Edinburgh, Univ. of Canterbury (New Zealand), Aix-Marseille Université (Morlet Chair), ETH Zürich, DTU Copenhagen and TU München. Currently, he is a visiting professor at the Charles University in Prague. He published more than 130 scientific papers. His work was cited more than 2300 times by more than 800 authors according to Mathematical Reviews.

Its **program** consists of a **one-hour lecture** followed by a **discussion**. The lecture is based on an (internationally) exceptional or remarkable achievement of the lecturer, presented in a way which is comprehensible and interesting to a broad computer science community. The lectures are in English.

**The seminar** is organized by the organizational committee consisting of Roman Barták (Charles University, Faculty of Mathematics and Physics), Jaroslav Hlinka (Czech Academy of Sciences, Computer Science Institute), Michal Chytil, Pavel Kordík (CTU in Prague, Faculty of Information Technologies), Michal Koucký (Charles University, Faculty of Mathematics and Physics), Jan Kybic (CTU in Prague, Faculty of Electrical Engineering), Michal Pěchouček (CTU in Prague, Faculty of Electrical Engineering), Jiří Sgall (Charles University, Faculty of Mathematics and Physics), Vojtěch Svátek (University of Economics, Faculty of Informatics and Statistics), Michal Šorel (Czech Academy of Sciences, Institute of Information Theory and Automation), Tomáš Werner (CTU in Prague, Faculty of Electrical Engineering), and Filip Železný (CTU in Prague, Faculty of Electrical Engineering)

**The idea to organize this seminar** emerged in discussions of the representatives of several research institutes on how to avoid the undesired fragmentation of the Czech computer science community.