Why is Fast Fourier Transform applied to raw EEG data?
Fast-Fourier Transform (FFT) transforms a signal from the time domain into the frequency domain. Basically, any time-dependent signal can be broken down in a collection of sinusoids. In this way, lengthy and noisy EEG recordings can be conveniently plotted in a frequency power-spectrum. By doing so, hidden features can become apparent. By adding all the sinusoids up after FFT, the original signal can be restored, so no information is lost. 

A notable application of FFT in EEG is shown in Fig. 1, which shows an EEG in an awake person (top blue trace) and an EEG in a propofol-sedated person (bottom red trace). The traces are different, but exactly how different? Scientists like to quantify stuff. 

Now look in Fig. 2, which shows the same data but filtered in the delta band (low-pass filtered EEG with a cut-off frequency of 1.5 Hz, left panel). Here it already becomes more apparent what's going on, but what exactly is the difference between the two traces? That difference becomes readily apparent in the frequency domain by using FFT (Fig. 2, right panel); The frequency spectrum has a peak at 0.2 Hz in both traces, but that peak is about twice as big in the anesthetized state than in the normal state. In other words, the anesthetized brain reveals more low-frequency activity.


Fig. 1. Raw EEG of an awake person (blue) and propofol-anesthetized person (red). source: Wang et al (2014).


Fig. 2.  Filtered EEGs (&lt;1.5 Hz) of an awake person (blue) and propofol-anesthetized person (red) (left panel) and corresponding FFT spectra (right). source: Wang et al (2014).

This is reminiscent of the drowsiness encountered in slow-wave sleep; which is yet another example of why FFT is useful; various stages of sleep are markedly different in their EEG. For example, early stages of sleep are characterized by slow-wave EEG, while REM sleep is characterized by high-frequency EEG activity. By using FFT, these differences in frequency content can be captured in simple, quantifiable data.     

Another widely applied FFT-based application is filtering in the frequency domain. Look at the sleep EEG in Fig. 3. By splitting the raw signal up in frequency bands, the noise can be removed (high-frequency components), but even better, the k-complex (a characteristic hallmark of normal sleep) can be beautifully isolated from a messy EEG signal (bottom trace, 12-15 Hz).


Fig. 3. EEG FFT-based filtering. source: Neurology  

Reference
- Wang et al., Front Syst Neurosci (2014); 00215