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Hans George Feichtinger - Computational Aspects of Time-Frequency and Gabor Analysis

24 Jan 2019   16:16-18:16

The thirty-ninth meeting of the Prague computer science seminar

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.

Posluchárna S5, MFF UK Malostranské nám. 25, Praha 1
Katedra kybernetiky FEL ČVUT
Contact person
Mgr. Helena Houšková
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