|
NuHAG :: TALKS
Talks given at NuHAG events
|
|
|
|
Gabor Analysis and Gabor Multipliers with a Musical Signal Processing Perspective Hans G. Feichtinger given at Queen Mary University of London, Dept. of Elect. Engin. (14.02.08 16:15) id: 935 length: 50min status: accepted type: invited LINK-Presentation: ABSTRACT:
There is a very natural interpretation of time-frequency analysis as displaying the energy of a (musical) signal over a time-frequency plane, the coordinates telling the ``viewer’’ at which time within the signal which harmonic components are of high relevance. Depending on the instrument it is possible to use more or less image processing methods to recognize the melody played. While the continuous representation is easy to understand the discretized version (going back to D.Gabor, 1946) is far less obvious. We know know that for ``any decent atom’’ (think of a tone which can be played in time and can be transposed to a sufficiently dense micro-tonal progression in the frequency domain) one can represent ARBITRARY signals (of finite energy) exactly on this micro-tonal ``pioano” (resp.\ DSP, because one might need more than 10 fingers!). The basic facts of Gabor multipliers and its potential for musical signal processing, in particular the role of Gabor multipliers, will be presented. All the theoretical findings can also be realized using the NuHAG Gabor toolbox (see www.nuhag.eu).
|