Problem 6 (Fourier Transform)

Your professor requires you to make an EEG (electroencephalogram: electrical activity of the brain)

recording and signal analysis. Certain EEG frequency bands have been defined where the gamma band

includes the highest frequencies. It includes frequencies of 30 100 Hz.

6.a) Assuming there is no noise and no filtering considerations, what is the required sample rate according to

Nyquist?

In order to make preliminary analyses, a Fourier Transform with a resolution of 1 Hz in the frequency

domain is required.

6.b) Which implications does this requirement have for the duration of the recording(s)?

It was chosen to record the signal with a sample rate of 500 Hz and in epochs (triggered repeated

recordings) of 2-second duration.

6.c) Sketch the coordinate axes that would be used to plot the full Fourier Transform of an epoch. Add units

to both axes and state the range and frequency resolution of the transformed signal.

In the FT of the signal it was found, that the frequency 20 Hz had a normalized value of 1, whereas the

frequency 8 Hz had a normalized value of 2.5.

6.d) Explain what these normalized values mean for the two frequencies in the time domain.