Since Electroencephalogram (EEG) signals have very small magnitude, it's very hard to capture these signals without having noise (produced by surrounding artifacts) affect the real EEG signals, so it is necessary to use Filters to remove noise. This work proposes a design of an electronic circuit using a microcontroller, an instrumentation amplifier and an operational amplifier able to capture EEG signals, convert the captured signals from analog state to digital one and send the converted signal (digital signal) to a group of three digital filters. This paper gives a design of three digital elliptic filters ready to be used in real time filtering of EEG signals (which preliminary represents the condition of the brain) making the software part which complements the hardware part in the EEG signals capturing system. Finally we are going to show the way of using the designed electronic circuit with the three designed digital filters, demonstrate and discuss the results of this work. We have used Eagle 6.6 software to design and draw the circuit, CodeVision AVR 3.12 software to write the program downloaded on the microcontroller, Mathworks MATLAB 2014a software to design the three digital filters and Mathworks MATLAB 2014a Simulink tool to make the appropriate experiments and get the results.