This thesis is about time-frequency analysis of the brainstem auditory evoked potential (BAEP). The work can be divided into two parts. One part where a model is built up from a very simple example to a more complex model resulting in a model consisting of a sum of sinusoids with stochastic starting points and amplitudes. Dierent time-frequency methods have been evaluated for these models and the multi window spectrogram with Hermitian base functions performs the best in a real life situation with more than one component and a high level of noise. The second part consists of investigating real BAEP data. BAEP data from ve patients were available. Each patient has two data sets which have been studied. One while the patient is awake and one while it is asleep. A hypothesis is that there exists some sort of dierence between these two datasets. It turns out that it does. The earlier peaks dier slightly in latency and the later peaks for the sleeping data seem to disappear. This result is concluded from dierent time frequency methods, where the spectrogram and the multi-window spectrogram are the most successful methods. An attempt to make a bootstrap simulation in order to estimate the mean and condence bounds of each peak is also made for one dataset
