Reconstruction of Sampled Signals with Fractal Functions

This paper proposes a procedure to build a fractal model for real sampled signals like financial series, climatic data, bioelectric recordings, etc. The mapping constructed owns in general a rich geometric structure. In a first step, the method provides a truncate Chebyshev approximant which performs a low-pass filtering of the signal, displaying in this way the leading cycles of the phenomenon observed. In the second, the polynomial is transformed in a fractal object. The Lipschitz properties of the original signal guarantee a good approximation of the represented variable, whenever the sampling frequency is high enough.