Fractal and Smooth Complexities in Electroencephalographic ProcessingNavascués MA1*, Sebastián MV2 and Valdizán JR3
- *Corresponding Author:
- Navascues MA
Departmento de Matem´atica Aplicada
Escuela de Ingenier´ia y Arquitectura
Universidad de Zaragoza, Spain
E-mail: [email protected]
Received November 06, 2014 Accepted December 31, 2014 Published January 10, 2015
Citation: Navascués MA, Sebastián MV, Valdizán JR (2015) Fractal and Smooth Complexities in Electroencephalographic Processing. J Appl Computat Math 4:198.doi: 10.4172/2168-9679.1000198
Copyright: ©2015 Navascués MA, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
The importance of the electroencephalogram (EEG) rests upon the fact that it provides useful information of the normal and pathological brain functions. However, the relations among abnormal EEG, brain functions and disorders are not well known yet. We have proposed numerical quantifiers of the EEG signal, coming from the methodology of fractal mathematics and the theory of approximation. In the first part we describe an alternative to the computation of nonlinear dimensions for this kind of signals. The approach used here is based on a fractal interpolation of the data. In the second part, we describe a method for the computation of smooth complexities based on the interpolation of EEG signals by means of polynomial splines. This kind of functions is used to find quadrature formulas for the spectral moments. Both procedures are applied to treat the electroencephalographic discrimination of a group of children suffering from an Attention Deficit with Hyperactivity Disorder (ADHD).