# The Blue Frog in the EEG

Alpha, beta, gamma what?  Spectral decomposition of the EEG signal may lose critical information.

In 1924 when Hans Berger first found a signal from the brain using scalp electrodes, the first structure that was evident to the eye was a regular rhythm at roughly 10 Hz. He called this the alpha rhythm. This began a search for brain rhythms or oscillations. Oscillations are repetitive elements of the signals, predictable up and down movements at a standard rate. And indeed oscillations abound.

The Fourier Transform

In 1805 Jean-Baptiste Fourier came up with an ingenious and delightful method for decomposing a wave into its component sine waves or harmonics, emerging out of his study of fourier series, which are complex periodic functions. Indeed it has tremendous applications across a variety of fields that use sinusoidal waves such as electrical engineering and analog communication systems. The method allows one to create a power spectrum, essentially a decomposition of the signal into its frequency components so that you can see which frequencies the waveform is composed of and in what proportion.

The EEG is also a time series and with the hint of oscillating components so researchers jumped on the bandwagon to make use of the latest signal processing technique. So much so that much of EEG analysis today rests on decomposition of the EEG signal into its spectral components (the frequencies it is composed of) using the fourier transform.

This would be sufficient as an approach if it were that the brain simply produced a mix of oscillations that had to be parsed (read What does the EEG signal measure?). However, oscillations are not the only aspect of the signal and certainly not the dominant aspect. Much of the signal is a complex temporal pattern, often riding on top of oscillations.

Beyond Oscillations

Taking the EEG wave and decomposing it into its component frequencies gives rise to a decreasing function– a ‘1/f’ like spectrum indicating the wide range of frequencies represented in the wave that are typically not oscillating at all but interspersed in complex patterns throughout the wave. The field of EEG decided to draw some somewhat arbitrary lines along this spectrum and name them alpha, beta, gamma etc., each representing a range of frequencies. (alpha as 7-15, though some use 8-14 or 7.5 to 12.5 its all pretty rough). This is shown in the graph below (the two lines are just two different electrodes).

It is not entirely without logic however, since sometimes there are bumps in the power spectrum where the oscillations are strong enough to be visible above the 1/f-like component so these lines have been drawn roughly in line with the way these bumps tend to frequently show up – like in the image below.

That said, when applied to the larger non-oscillating part, it is entirely arbitrary. Unfortunately, today much of the literature fails to distinguish between true oscillations and the 1/f component, lumping them all together as rhythms and speaking of them as ‘waves’. This is bad for several reasons. The patterns produced in the EEG are a complex mix of frequencies in time in the same way that a picture is a complex mix of colors in space and may not be periodic waves at all.

Lost Information

A spectral decomposition of the signal can be thought of as similar to analyzing a work of art by transforming it into its color spectrum and describing it in terms of how much red, blue and green is in it. You lose the important information of how they mix and which color is next to which. If you looked at a lot of pictures this way you might come up with some inference such as ‘pictures with lots of blue means it is a picture of the sky’ and it might indeed be statistically significant that when you compared pictures dominated by blue to pictures dominated by red that the blue ones more likely represented sky. However, while color composition is certainly an aspect of a painting, you would miss the larger point of a Monet or Renoir or the blue frog in the picture above.

However, this is the same way that we make inferences about the EEG with studies that show things like ‘more ‘beta’ means you are more alert’. The thoughts we produce are far more than simply the few permutations allowed by changing levels of five arbitrary frequency ranges. Simply looking at relative levels of broad bands of frequencies perhaps misses the point of the immense art of the human brain.

Can we go beyond this to methods that are more discriminating of the contours of the picture? More in upcoming posts.