Indiana University-Purdue University Indianapolis (IUPUI) / A Brain Computer Interface (BCI) is a hardware and software system that establishes direct communication between human brain and the environment. In a BCI system, brain messages pass through wires and external computers instead of the normal pathway of nerves and muscles. General work ow in all BCIs is to measure brain activities, process and then convert them into an output readable for a computer. The measurement of electrical activities in different parts of the brain is called electroencephalography (EEG). There are lots of sensor technologies with different number of electrodes to record brain activities along the scalp. Each of these electrodes captures a weighted sum of activities of all neurons in the area around that electrode. In order to establish a BCI system, it is needed to set a bunch of electrodes on scalp, and a tool to send the signals to a computer for training a system that can find the important information, extract them from the raw signal, and use them to recognize the user's intention. After all, a control signal should be generated based on the application. This thesis describes the step by step training and testing a BCI system that can be used for a person who has lost speaking skills through an accident or surgery, but still has healthy brain tissues. The goal is to establish an algorithm, which recognizes different vowels from EEG signals. It considers a bandpass filter to remove signals' noise and artifacts, periodogram for feature extraction, and Support Vector Machine (SVM) for classification.