How can you get time related to frequency domain behavior? [FourierTransform, SignalProcessing, PowerSpectralDensity]

Question

Context: Data shown is EEG Time domain data transformed to get an alpha brainwave plot with X= Time Units & Y= Intensity/Power of the frequency band of interest.

Question: how do you get time data on the x axis after the FourierTransform or after PowerSpectralDensity? Isn't the time data lost, when you do the Fourier Transform?

How can you get the time data related to different brainwave intensities, if you've already done the Fourier Transform?

Expected Plot-types: Plots I would have expected for a procedure like this, shown below.

• PowerSpectralDensity = FFT (Autocorrelation of a Time Series DataSet)

• FFT or FT of Time Domain Data

Also... a related question I have on the DSP StackExchangeSite on Autocorrelation for EEG Signal Processing: Processes/Transforms involved to get brainwave data from raw EEG? (Autocorrelation confusion)

Thanks!

Answer 1

In the red alpha line graph:

X Axis = Time (in seconds) Y Axis = Power/Intensity (from the Fourier Transform)

You can know the power within certain time frames, because of windowing, like [welch windows][1].

The raw EEG data was segmented and broke into windows of a window length of time n.

The graph shows alpha powers @ a window. [1]: https://en.wikipedia.org/wiki/Welch%27s_method