Changes in a person's mental, emotional and psychological state are accompanied with different changes in brain activity. Brain activity is a result of synchronous electrical activity of numerous nervous cells in the brain (neurons). Electroencephalography (EEG) is a noninvasive method to record electrical activity of the brain, using the electrodes placed along the scalp. EEG contains five characteristic brain waves (alpha, beta, gamma, theta and delta waves). Alpha waves predominantly originate from the occipital lobe during wakeful relaxation and their amplitude is increased with closed eyes. Higher alpha wave levels are often linked to higher creativity, better memory and faster problem solving skills. The biofeedback method is based on the conscious control of physiological functions that are usually under the control of the autonomic nervous system, such as brain waves, heart rate and pain perception. Application of alpha waves in the biofeedback method enables treatment of hyperactivity disorders and speech problems in younger children and lately it is used more often in other fields of medicine and psychology. A high-quality, reliable and fast method of extraction of an alpha rhythm from an EEG signal is a prerequisite for further research. Two of the often applied methods in the analysis of EEG signals are the Fourier and Wavelet transform. While the standard Fourier transform is only localized in frequency, the Wavelet transform is localized in both time and frequency, which is important in the processing of real, non-stationary signals, such as EEG. In literature, those two methods are sometimes used in combination, so that their shortcomings are compensated for. As part of this thesis, Wavelet transform is analyzed as well as the combination of the Wavelet and Fourier transform, with the purpose of extracting an alpha rhythm. Also, three different prototype functions (Daubechies (Db4), Symlets (Sym9) i Coiflets (Coif5)) and two threshold calculation methods are tested. In total, nine different algorithm designs were tested on EEG signals recorded with three electrodes, with the sampling frequency of 200 Hz. Based on the number of false detections, three methods are chosen for further analysis. The chosen methods are then compared based on the runtime, sensitivity and correlation coefficient and given the results, method num. 2 was proposed as the most appropriate method for real time analysis of EEG signals. Method num. 2 is based on the Wavelet transform (Db4). The final result of this thesis is a simple GUI application for alpha rhythm detection, developed in Matlab. The application provides real-time feedback on alpha wave \linebreak levels, based on measured brain activity. During alpha rhythm detection the application uses the proposed method num. 2 that is based on the Wavelet transform (Db4). Wavelet transform, especially Db4 prototype, is often recommended in literature as the best method for the EEG signal analysis, which is consistent with the results obtained in this thesis.