Download A Reduced Multiple Gabor Frame for Local Time Adaptation of the Spectrogram In this paper we propose a method for automatic local time adaptation of the spectrogram of an audio signal, based on its decomposition within a Gabor multi-frame. The sparsity of the analyses within each individual frame is evaluated through the Rényi entropies measures. According to the sparsity of the decompositions, an optimal resolution and a reduced multi-frame are determined, defining an adapted spectrogram with variable resolution and hop size. The composition of such a reduced multi-frame allows an immediate definition of a dual frame: re-synthesis techniques for this adapted analysis are easily derived by the traditional phase vocoder scheme.
Download Sound Analysis and Synthesis Adaptive in Time and Two Frequency Bands We present an algorithm for sound analysis and resynthesis with local automatic adaptation of time-frequency resolution. There exists several algorithms allowing to adapt the analysis window depending on its time or frequency location; in what follows we propose a method which select the optimal resolution depending on both time and frequency. We consider an approach that we denote as analysis-weighting, from the point of view of Gabor frame theory. We analyze in particular the case of different adaptive timevarying resolutions within two complementary frequency bands; this is a typical case where perfect signal reconstruction cannot in general be achieved with fast algorithms, causing a certain error to be minimized. We provide examples of adaptive analyses of a music sound, and outline several possibilities that this work opens.