CONSTRUCTING AN INVERTIBLE CONSTANT-Q TRANSFORM WITH NONSTATIONARY GABOR FRAMES
Gino Angelo, Gino Angelo Velasco, Nicki Holighaus, Monika Dörfler, Thomas Grill · 2011
An efficient and perfectly invertible signal transform feat uring a constant-Q frequency resolution is presented. The proposed approach is based on the idea of the recently introduced nonstationary Gabor frames. Exploiting the properties of the operator corresponding to a family of analysis atoms, this approach overcomes the problems of the classical implementations of constant-Q transforms, in particular, computational intensity and lack of i nvertibility. Perfect reconstruction is guaranteed by using an easy t o calculate dual system in the synthesis step and computation time is kept low by applying FFT-based processing. The proposed method is applied to real-life signals and evaluated in comparison to a related approach, recently introduced specifically for audio signa ls.