title: Theory, implementation and applications of nonstationary Gabor frames.
abstract: 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.
authors.affiliation: Acoustics Research Institute, Austrian Academy of Sciences, Wohllebengasse 12-14, 1040 Wien, Austria.
authors.forename: P
authors.initials: P
authors.lastname: Balazs
authors.forename: M
authors.initials: M
authors.lastname: Dörfler
authors.forename: F
authors.initials: F
authors.lastname: Jaillet
authors.forename: N
authors.initials: N
authors.lastname: Holighaus
authors.forename: G
authors.initials: G
authors.lastname: Velasco