On the Structure of the Phase around the Zeros of the Short-Time Fourier Transform
Résumé
The short-time Fourier transform is a time-frequency representation widely used in audio signal processing. At first sight, the phase of the transform may appear to be difficult to interpret, a fact that led to the development of many processing schemes in audio processing relying on the modulus of the transform only. However, it has been shown, that the phase information can be successfully exploited for improved analysis and processing. This is illustrated for example by the reassignment method or the phase vocoder algorithm. In order to better exploit the phase information in audio processing, a better understanding of its structure is desirable. This study describes a particular behavior of the phase which can be observed when looking at the phase derivative over time or frequency around the points where the transform equals zero. This recurrent behavior is illustrated using numerical simulations on synthesized and real audio signals. The performed simulations show the influence of the parameters of the transform on the observed structures. Some consequences of this phase structure for audio processing are also presented.
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Licence : Copyright (Tous droits réservés)
Licence : Copyright (Tous droits réservés)