## Section: Application Domains

### Speech signal

Participants : Hussein Yahia, Khalid Daoudi, Oriol Pont, Vahid Khanagha, Antonio Turiel, Régine-André Obrecht, Alex Potamianos, Petros Maragos, Ioanis Klasinas, Reda Jourani.

Some specialists in speech signal analysis have been interested in the use of Lyapunov exponents and other considerations from deterministic chaotic systems applied to such signals, to measure their chaotic behaviour and adapt the analysis accordingly.

First, researches in GEOSTAT focus on demonstrating the turbulent character of speeh signal, because of its formation processes, and, as we noted earlier, classical Lyapunov exponents are insufficient for deriving entirely this character. Then, GEOSTAT will focus in developping, for speech signal analysis, the necessary tools in the Microcanonical Multiscale Formalism that will take into account efficiently the non-linear aspects of these signals and adapt the recognition and classification methods accordingly. Hence the first step consists in understanding the signification of singularity exponents for speech signals, and to adapt the MMF for deriving meaningful geometric super-structures from these signals. Speech signals need a complete re-writing of some procedures used in the MMF, for instance by taking into account finite variable window sizes associated to the computation of singularity exponents and the observation of source field. Then, a vast research programme will consist in understanding and adapting the framework of reconstructible systems, and to derive the methods for analysis, classification and recognition. The study of speech signal will be the occasion, in GEOSTAT, of understanding subtle aspects specific to 1D-signals, to derive generic models for temporal series, and to study temporal evolution in a simplified case.