In this work, we look for methods providing a local variation of the time-frequency resolution for sound analysis and re-synthesis. In Time-Frequency Analysis, adaptivity is the possibility to conceive representations and operators whose characteristics can be modeled according to their input: the first objective of this work is the formal definition of mathematical models whose interpretation leads to theoretical and algorithmic methods for adaptive sound analysis. The second objective is to make the adaptation automatic; we establish criteria to define the best local time-frequency resolution, with the optimization of appropriate sparsity measures. To be able to exploit adaptivity in spectral sound processing, we then introduce efficient re-synthesis methods based on analyses with varying resolution, designed to preserve and improve the existing sound transformation techniques. Our main assumption is that algorithms based on adaptive representations will help to establish a generalization and simplification for the application of signal processing methods that today still require expert knowledge. In particular, the need to provide manual low level configuration is a major limitation for the use of advanced signal processing methods by large communities. The possibility to dispose of an automatic time-frequency resolution drastically limits the parameters to set, without affecting, and even ameliorating, the treatment quality: the result is an improvement of the user experience, even with high-quality sound processing techniques, like transposition and time-stretch.
