A relation between fractal dimension and Fourier transform – electroencephalographic study using spectral and fractal parameters

Abstract

Fourier parameters display the spectral content of a signal and provide explicit representations in the frequency domain. In the case of electroencephalograms, the FFT algorithm was the only quantifying method used until the 1970s, but this analysis is not conclusive in most pathologies. Fractal techniques provide new tools for the processing of signals whose traces have a sophisticated geometric complexity. The fractal dimension is computed easily in our work by means of explicit formulae involving the time samples. In this paper we obtain, under some hypotheses, an exact relation between the Fourier Transform of a signal and its Fractal Dimension. In the last part of the paper, an electroencephalographic application involving fractal and spectral parameters is described.

Keywords:

• Fractals
• Iterated function systems
• Fractal interpolation functions
• Fourier transform
• Fractal dimension