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The recognition of epileptic waveforms from the electroencephalogram is an important physiological signal processing task, as epilepsy is still one or the most frequent brain disorders. The main goal of this paper is to present a new method to diagnose the epileptic waveforms directly from EEG, by performing a quick signal processing, which makes it possible to apply in on-line monitoring systems. The EEG signal processing is performed in two steps. In the first step, by using the multi-resolution wavelet decomposition, we obtain different spectral components (α, β, δ, θ) of the measured signal. These components serve as input signals for the artificial neural network (ANN), which accomplishes the recognition of epileptic waves. The recognition rate for all test signals turned out to be over 95%.