### High Frequency Brain Signals (HFBS) in EEG and MEG, Part Two: A scientific hypothesis

Last week, I wrote a blog post about High Frequency Brain Signals (HFBS) in EEG and MEG. In that post, I made an assumption that the HFBS we observed might be introduced by windowing function. Of course, I do not have any support to prove nor to disprove this assumption.

Today, I will explain why HFBS is a scientific hypothesis.

The signal in each  M/EEG (EEG or MEG) channel is the composition of activities of thousands or millions of neurons. Limited by the mechanism that neurons fire, one neuron won't generate HFBS - at least not those at hundreds of Hertz. When thousands or millions of them all fire, and the composition happens to be non-linear, things could be different.

For example, from basic trigonometry, we know that:
$$\sin(2x) = 2\sin(x)\cos(x)$$ and $$\cos(2x) = \cos^2(x) - \sin^2(x)$$
See? The frequency is doubled on the left hand side of the two equations.

If multiplication between brain signals could happen, then we can get signals of higher frequency. In physics and electrical engineering, such higher frequency signals are called harmonics and are related to a very annoying trouble in communication systems: intermodulation noise/distortion. Can you guarantee that our brain is a linear system?

Since neurons do not fire independently (many papers are discussing synchrony and connectivity of the brain), it's reasonable to assume that multiplication and even more complicated operations could happen on signals from neurons. Such composed signals are captured by M/EEG.

Therefore, it is scientific to hypothesize that HFBS is real from the brain, not introduced by sampling techniques. In this sense, HFBS is a useful tool to study how our brain works.

Comments are welcome, especially those from DSP or neuroscience field.