Theory, implementation and applications of nonstationary Gabor frames

نویسندگان

  • Péter Balázs
  • Monika Dörfler
  • Florent Jaillet
  • Nicki Holighaus
  • Gino Angelo M. Velasco
چکیده

Signal analysis with classical Gabor frames leads to a fixed time-frequency resolution over the whole time-frequency plane. To overcome the limitations imposed by this rigidity, we propose an extension of Gabor theory that leads to the construction of frames with time-frequency resolution changing over time or frequency. We describe the construction of the resulting nonstationary Gabor frames and give the explicit formula for the canonical dual frame for a particular case, the painless case. We show that wavelet transforms, constant-Q transforms and more general filter banks may be modeled in the framework of nonstationary Gabor frames. Further, we present the results in the finite-dimensional case, which provides a method for implementing the above-mentioned transforms with perfect reconstruction. Finally, we elaborate on two applications of nonstationary Gabor frames in audio signal processing, namely a method for automatic adaptation to transients and an algorithm for an invertible constant-Q transform.

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عنوان ژورنال:

دوره 236  شماره 

صفحات  -

تاریخ انتشار 2011