In recent years, some novel methods have been developed for the detection of diseases based on biomedical signals. In this article, a method for the automated detection of epilepsy seizures is presented by analyzing electroencephalogram (EEG) signals based on the wavelet transform. In the first step, the EEG signals are pre-processed with the Savitzky-Golay filters (SGF) for noise elimination. The filtered signals are decomposed with Discrete Wavelet Transform (DWT) to construct spontaneous alpha and beta brain rhythms. The mean, standard deviation, skewness, kurtosis, energy and entropy characteristics are extracted from healthy and seizure intervals. By using support vector machine (SVM), the signals are classified in the categories of normal and epileptic, reaching precision levels of 92.82% in the alpha rhythm in comparison with other previous works.