In our spectral features post we used the height example: 1.85 metres is how my height is expressed in the metric system, and the Fourier transform moves a signal into another unit system, the frequency domain. In this post we don’t change the unit system at all. We read the signal as it was recorded, along the time axis.
Summarising A Road Trip
Imagine a long drive where your speed is logged every second. Thousands of numbers. But to tell someone about the trip, you don’t need to read them all out. A few summaries are enough:
- What was your average speed?
- How much did your speed vary? Did you cruise steadily, or keep speeding up and slowing down?
- How many times did you stop and start?
- Were there any sudden brakes?
We ask the same questions of EEG. We call the answers temporal or time-domain features.
The Basics
- Mean and amplitude: how large the signal’s swings are. Peak-to-peak amplitude is the gap between the highest and lowest values.
- Variance: how much the signal fluctuates around its mean. It’s directly related to the signal’s energy.
- Zero-crossing count: how many times the signal crosses the zero line in a given time. Without any Fourier transform, it gives a rough but fast idea of how quickly the signal oscillates. Like “how many times did you stop and start?”.
- Skewness and kurtosis: does the signal swing evenly, or does it occasionally shoot up in sudden sharp peaks, like sudden brakes? Useful for catching sharp events such as epileptic discharges.
Hjorth Parameters
In 1970, Bo Hjorth proposed three parameters that summarise EEG entirely in the time domain. They’re still widely used:
- Activity: how “loud” the signal is, i.e. its variance.
- Mobility: the signal’s average tempo; how quickly it changes.
- Complexity: how closely the signal resembles a pure sine wave. The higher the value, the more irregular the signal.
Interestingly, these three numbers also carry information about frequency. But none of them needs a Fourier transform, so they’re very fast to compute.
Event-related Potentials
Perhaps the most powerful tool in the time domain is the event-related potential (ERP). We show a participant the same kind of stimulus dozens of times, take the few hundred milliseconds of EEG right after each one, and average them together.
Picture a crowded hall where everyone is chatting at random, while one group keeps whispering the same sentence over and over. You can’t hear it once. But stack a hundred recordings on top of each other and the random chatter cancels out, while the repeated whisper stands out. In an ERP, the brain’s consistent response to a stimulus emerges from random activity in the same way. For example, the P300 wave, appearing about 300 milliseconds after a stimulus, is associated with attention and unexpected events.
Why Does It Matter?
Temporal features are easy to compute, intuitive to interpret and fast enough for real-time applications. Most studies use them alongside spectral features: one answers “how much of which rhythm?”, the other “how does the signal behave over time?”.
In the next post we’ll move to a third point of view: fractal features, which measure how “rough” a signal is.
References
- Hjorth, B. (1970). EEG analysis based on time domain properties. Electroencephalography and Clinical Neurophysiology, 29(3), 306–310. DOI: 10.1016/0013-4694(70)90143-4