In this paper, we propose a new approach for modeling speech signals. The principle of this approach consists in using a generalisation of iterated functions systems theory (IFS) to give a robust functional representation of speech signals, based on the analysis of the local regularities of the waveforms. This approach is motivated by the fact that the local singularities, measured in terms of H�lder exponents [1], contains crucial information on the voice signal. We show that this technique allows to describe some characteristic features of the speaker and to build a parsimonious model of the speech signal, which permits to synthesize it with a good accuracy.