39. Prague Computer Science Seminar
Gabor analysis is a part of timefrequency analysis concerned with localized
Fourier expansions of a given signal. In the onedimensional 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
picturesobtained by this transform, spectrograms, look like a graphical
composition.
Themethod 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 speakerâ€™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.
