# Types of brain waves

Brain waves - hmm sounds a bit damp - but this is a commonly used description of the tiny electrical signals that can be recorded at the scalp of subjects undergoing electroencephalogram (EEG) signal measurement. In this article we take a look at the so-called **types of brain waves** that are seen in a typical EEG recording.

If like me you have been around for a while you might remember the time when radio stations were describds as broadcasting in the Light Wave band, Medium Wave band and so on. We understood that this had something to do with frequency. It's the same with EEG which we will see is sometimes described as having certain "wave properties" that we associate with a range of frequencies.

The EEG is a biolectric potential that can be recorded from the surface of the head using appropriate electrodes and instrumentation. When this is done as part of a neurofeedback session one or two carefully selected locations on the scalp might be used. If the aim is to collect QEEG (quantitative EEG) data then the **10-20 standard** describes the locations of 24 electrode positions.

The signals are time varying patterns of electrical energy that are typically in the microvolt range. They are consequntly hard to measure unless you pay careful attention to the characteristics of the hardware as well as preparation, the types of electrodes, conductive gels etc.

Characteristic patterns of EEG have been associated over the years with different stages of sleep, levels of arousal, meditation, epileptic seizures, and drug induced states. The EEG is not in itself there for any physiological reason but is certainly a reflection of underlying brain states.

The communication between the billions of neurons in the brain is now recognised to be an electro-chemical event. In the past, operational theories tended to focus either on chemical or electrical models of function but these are not important for our discussion.

The fact is, the electric potential of a large number of neurons (specifically the pyramid cells in the cortex) can be measured and related to brain states. What we observe with the EEG is the sum of the post-synaptic potentials.

The first recording of the EEG signal took place back in 1929. Obviously they could not benefit from the modern hardware and processing capability we have now, so it is impressive that these very small signals - of the order of tens of microvolts - could be measured with any fidelity. Within ten years the characteristic components of the EEG had been described as the **delta, theta, alpha and beta frequency wave bands** that are still often used today. But what does this actually mean?

## Fourier series idea

Imagine for a moment the challenge of describing the raw EEG signal elegantly. Inspecting the recorded raw EEG signal back in 1929 we would have probably seen this recorded on a chart showing a complex, varying-amplitude, continuous-time signal. It's literally indescribable using words.

Suppose for a moment we wanted a method to describe this signal in an unambiguous way. Using the universal language of mathematics it becomes possible to do exactly this.

Imagine you were on the telephone to someone and tried to describe a particular EEG recording to them. It would be a challenge to do this with any degree of accuracy. Take a look at the EEG signal above and you will get an idea of the challenge involved in doing this.

Of course, this type of problem is not new and mathematicians a long time ago got to grips with it. They weren't thinking of EEG in particular but just about the properties of anything that varied over time - it could be crop yields, temperature changes in the arctic, sea levels in the harbour or stock market prices - the approach would be largely the same.

In the 1800's a **French mathemetician called Fourier** worked out how to more accurately describe patterns of change (specifically the technique is for situations where patterns repeat in a cyclic or close to cyclic fashion) in a way that was both concise and elegant.

**He used what we call "basis functions" to describe what we don't know (the original waveform) in terms of what we do know.**

Fourier used sine waves and cosine waves as basis functions along with a method of choosing them so that the error between the true signal and his estimate reduced as more terms (sine and cosine waves) were added Any sine wave or cosine wave can be completely described if we know it's magnitude and frequency so these are very convenient basis functions. Everybody who knows the language of mathematics is good to go.

Fourier's method aimed to choose these basis functions - producing a series of sine waves or cosine waves of different magnitudes and frequencies which if added together would produce an approximation to the original signal. The more terms included in the Fourier series, the better the approximation of course.

Some authors have described the Fourier series approach as like using a prism to split an origianl beam of light into a spectrum of colours (the frequenct waves of spectrum)

In this metaphor, the original beam of white light can be split into its constituent colours of Red, Yellow, Orange, Green and so on. Each colour has a particular frequency on the electromagnetic spectrum.

The Fourier series method, in our context, splits the original EEG signal into its frequency components.

Generally we find that the amplitude of the lower frequency components is higher than the higher frequency components. Today we tend to use digital computers for signal processing rather than charts but the principle is the same.

Computers can't handle things that are continuous in time. Even the shortest duration of data could not be represented in a digital computer unless it was sampled first. In fact data acquisition systems such as the NeXus series sample continuous in time signals (via the sample rate) and they "sample" in magnitude (by the number of bits of resolution).

Although it's not quite so elegant as the white light split by a prism, the Fourier method allows us to split the raw EEG into different a number of so-called frequency bands that have been given names over the years as shown below.

When setting up for data acquisition with BioTrace and the NeXus devices, some of the settings such as sample rate and signal resolution will have default settings that are appropriate to the situation. With a click of a button you can calculate an FFT (Fast Fourier Transform) which is a software (digital) implementation of Fourier's method. This lets you imagine the original waveform split into the "frequencies" which can be classified and refined in many ways.

This is a lot of power and capability but it doesn't remove the need to grasp the underlying meaning of what is happening technically. In other articles we will delve into various aspects of signal processing basics.

## Frequency Bands

What we have learned? The raw EEG is a low amplitude continuous-time signal that looks chaotic but can actually be represented as a set of sine wave basis functions in the frequency domain. The raw signal is sampled and converted into a discrete-time representation suitable for computer operations. The Fourier series approximation is implemented by a process referred to as the Fast Fourier Transform or FFT.

In this way, the raw signal is transformed into something in "the frequency domain". Notice how the general magnitude of the parts of the spectrum get smaller as the frequency increases. The lower trace has magnitude on the 'Y' axis and increasing frequency from left to right on the 'X' axis.

The following table gives a basic summary of the Frequency Bands and their association with particular functions. Of course the word descriptions are inevitably a bit ambiguous. By convention the Frequency Bands straddle the following frequencies

- DELTA - 2 - 4 Hz
- THETA - 4 - 8 Hz
- ALPHA - 8-12 Hz
- SMR 12-15 Hz
- BETA 1 15 - 21 Hz
- BETA 2 21 - 30 Hz
- GAMMA 30 Hz and up

## Limitation of the Notion of Bands

Historically the labels Delta, Theta, Alpha etc were assigned in the order in which they were discovered in the original research and limited by the technology of the time. There is nothing intrinsically "special" or physiologically significant about the bands. The frequency and amplitude of the EEG ultimately depends on the state of the brain (relaxed, alert etc), on the electrode location, on the task being carried out by a subject (reading, meditation etc) and on the individual's status (age, gender etc) - even the time of day.

We need therefore to be careful when using these brainwave labels. We need to at least state the location of the EEG electrode(s) and the frequency range in our observations otherwise we are not being specific enough.

By looking at the brain waves (frequency spectrum) across many locations of the subjects scalp, practitioners may recognise patterns that do not belong and devise neurofeedback sessions to influence change. That's a topic we explore in other articles