In this paper, we present a method for speech signal analysis and synthesis based on IFS theory. We consider a speech signal and the graph of a continuous function whose irregularity, measured in terms of its local Hölder exponents, is arbitrary. We extract a few remarkable points in the signal and perform a fractal interpolation between them using a classical technique based on IFS theory. We thus obtain a functional representation of the speech signal, which is well adapted to various applications, as for instance voice interpolation.