Early-Stage Pilot Study on Using Fractional-Order Calculus-Based Filtering for the Purpose of Analysis of Electroencephalography Signals
Abstract Analysis of Electroencephalography (EEG) signals has recently awoken the increased interest of numerous researchers all around the world with regard to rapid development of Brain-Computer Interaction-related research areas and because EEG signals are implemented in most of the non-invasive BCI systems, as they provide necessary information regarding activity of the brain. In this paper, a very early stage pilot study on implementation of filtering based on fractional-order calculus (Bi-Fractional Filters – BFF) for the purpose of EEG signal classification is presented in brief.
One may represent polynomials not only by their coefficients but also by arithmetic circuits which evaluate them. This idea allowed in the past fifteen years considerable complexity progress in effective polynomial equation solving. We present a circuit based computation model which captures all known symbolic elimination algorithms in effective Algebraic Geometry and exhibit a class of simple elimination problems which require exponential size circuits to be solved in this model. This implies that the known, circuit based elimination algorithms are already optimal.