Why is Fast Fourier Transform applied to raw EEG data?

Question

I am trying to understand why Fast Fourier Transform (FFT) is used in the analysis of raw EEG channel data.

My understanding (at the 30,000 ft view) is that FFT decomposes linear differential equations with non-sinusoidal source terms (which are fairly difficult to solve) and breaks them down into component equations (with sinusoidal source terms) that are easy to solve. It then combines each of these component/partial solutions to solve the original equation. In laymen's terms, it's like taking a smoothie, and breaking it down into its recipe of ingredients. Doing so would allow us to study and analyze each ingredient as it relates to the final product (the smoothie).

But how does this relate to raw (non-FFT-decomposed) EEG data? My understanding of a single channel of EEG data is that it is essentially a measurement of voltage over time. What is to be gained by using FFT to break this voltage/time signal down into its constituent frequencies (alpha/beta/gamma/delta/mu waves), etc.? What additional information can each frequency tell us about the raw data?

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Update:

Here is my updated understanding of how FFT relates to raw EEG data per @Mark's description below:

Answer 1

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 (<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}

<sub>Reference
- Wang et al., Front Syst Neurosci (2014); 00215</sub>

Answer 2

Any periodic waveform can be produced by adding up a series of sin waves of the appropriate frequency and amplitude. The FFT looks at a complex waveform and calculates those frequencies and amplitudes. The result is a new curve which plots amplitude vs frequency. Thus, it transforms the signal from the time domain into the frequency domain.

I don't have any knowledge of EEG signals, but have worked with FFTs. If you wanted to know what frequencies make the largest contribution to the original waveform, the FFT will provide that information.

Here is a paper I found which uses FFT analysis of EEG waveforms to look at the relative contributions of different frequencies. It includes the following table which indicates that "Delta" waves are in the 0.5 to 4 Hz range, Theta waves are in the 4 - 8 Hz range, etc. The FFT analysis quickly breaks the overall waveform down into its constituent frequencies to identify which of these ranges contribute the most or least.

Answer 3

EEG is simply measuring voltage fluctuations over the scalp caused by electric dipole(s) within the brain tissue. Communication between neurons can happen at different spatial and temporal scales. At each scale, this communication results in a distinct pattern of current flow. Because EEG measures voltage fluctuations over a relatively large patch of the brain, it reflects current flow created by communication at various scales between millions of neurons (each scale presumably associated with a different frequency of oscillations). Current research is attempting to understand what neural processes in the brain tissue result in the EEG. There is still not a complete understanding of what each frequency band represents, but studying similar types of oscillations within brain tissue (called local field potentials) have provided invaluable insights (for instance, small range communications are associated with higher frequency bands). How the oscillations recorded inside the brain tissue are related to the EEG is an active area of research.