A FRACTAL APPROXIMATION TO PERIODICITY

Abstract

Periodicity is recurrent in nature and society. The problem of the periodicity is faced here with the support of fractal methodology. Some analytical tools for the understanding of the one-dimensional projections of periodic phenomena are proposed. The reconstruction of an unknown periodic sampled variable is approached, assuming a deterministic self-affine nature in its small oscillations. Fractal trigonometric polynomials are defined by means of suitable iterated function systems. These objects are fractal perturbations of the classical circular functions. The coefficients of the system enable the control and modification of the properties of the originals. Additionally, Fourier parameters and approximants for sampled signals are computed and the density of the fractal trigonometric polynomials in the most common spaces of periodic functions is proved.