In simplistic introductory tutorials on the Fourier transform, you see examples of perfectly stationary signals ("stationary" means the statistical properties such as mean, variance, etc., remain the same over time). But brain activity is far from stationary! In fact, it is fairly accurate to say that neuroscientists are specifically interested in the brain's non-stationarities (for example, after seeing a visual stimulus or when recalling a specific memory).
In this video you will learn what happens in the frequency domain when the time-domain signal is non-stationary. And to quell suspense: The Fourier transform is always a perfect and useful reconstruction, even when the data violate stationarity. It is about 15 minutes long.
|Download the Matlab script for simulating and Fourierizing nonstationary time series data.|