EEG and frequency bands

Electroencephalography, or EEG, records voltage differences using electrodes. Frequency bands describe how quickly parts of a signal vary; they are not separate channels for particular thoughts.

Intuition: one trace, many time scales

A slowly varying signal can have faster oscillations superimposed on it. Separating these time scales helps describe a recording. The illustrative trace above is made from five known tones; a real scalp signal mixes sources, noise and artifacts and need not be periodic.

A voltage channel is defined relative to a reference. Changing the reference changes the recorded differences, so electrode names and a frequency label alone are not a complete acquisition description.

Frequency and sampling

A sinusoid is described by

$$x(t)=A\sin(2\pi ft+\phi),$$

where $A$ is amplitude, $f$ frequency in cycles per second, and $\phi$ phase. Sampling at rate $f_s$ observes $x(n/f_s)$. Without appropriate band limitation, frequencies above $f_s/2$ can alias into lower frequencies; a plot may look smooth and still misrepresent the signal.

In our teaching convention, delta is 0.5–4 Hz, theta 4–8, alpha 8–13, beta 13–30, and the displayed gamma interval is 30–45. Lower boundaries are included and upper boundaries excluded. Definitions vary across sources and tasks, and gamma is not limited to 45 Hz in general.

Associations are contextual

Delta is prominent during deep non-REM sleep. Theta often accompanies drowsiness; posterior alpha is often seen during relaxed, eyes-closed wakefulness. Faster beta and gamma activity require careful interpretation, including possible muscle contamination. A band name by itself does not establish mental state, diagnosis or the origin of a signal.

Power needs a convention too

For a finite sequence, mean-square amplitude is $N^{-1}\sum_n x_n^2$. Relating this to a spectrum requires a declared transform normalization and, often, windowing. Relative band power additionally depends on the frequency range chosen for the denominator. Two “alpha power” numbers may be incomparable if these choices differ.

Where you will see this

The band explorable documents its Fourier selection and limitations. The sleep project uses a documented preprocessing protocol and person-separated evaluation; the synthetic illustration is independent of that study.

References

• American Epilepsy Society: the normal EEG.
• MNE: filtering background and pitfalls.