Generalized IFS for Signal Processing

Several methods have been proposed to estimate theHölder exponents of signals [1, 4]. In this paper, we propose a new approach, based on a generalization of iterated functions system (IFS), which is well adapted to irregular continuous 1D signals. We also use these generalized IFS to build parsimonious models of complex signals and to perform segmentation on them. This paper is organized as follows : in section 2 we recall the definition of generalized iterated functions systems (GIFS) and the definition of the Hölder exponent of a nowhere differentiable continuous function. In section 3, we recall a result obtained in [2] concerning the Hölder exponents of the attractors of GIFS. We then propose a method to solve the inverse problem for GIFS and we use it to estimate the Hölder exponents of discrete signals. We present results obtained on generalized Weierstrass functions. In section 4, we develop a synthesis scheme for a given signal. The parameters of the GIFS, along with the Hölder exponents at different resolutions of the signal, allow to give a functional representation of discrete data. This in turn permits signal segmentation. An application on a residual speech signal is presented.