How to transform data to a frequency spectrum? Recently, I studied a paper called "What Does Your Chair Know About Your Stress Level?

It can be download at the link below.


  http://www.barnrich.ch/wiki/data/media/pub/2010_what_does_your_chair_know_about_your_stress_level.pdf


at page 210, Fig.5 (picture 5) mentioned that


  Spectra of the norm of the CoP vector during the experiment (stages 3–7) for the same subject used in Fig. 4.


How did they do to transform Fig.4 to Fig.5? And what do x-axis and y-axis mean in Fig.5?

Fig4


Fig5
In the cited paper their methodology is explained in the Materials and Methods section on  p.209, where it says:


  Fig. 4 shows the norm of the CoP during the experiment [...] which are represented by spikes in the norm of the CoP [...] In order to characterize the movement properties of the CoP, we have computed the corresponding spectra over the experiment stages [...]. Fig. 5 shows the spectra of the norm of the CoP [...].


Spectra, or more appropriately called frequency spectra or spectrograms, are typically generated by Fast Fourier Transformation (FFT). FFT essentially decomposes a signal into a collection of sine waves. The x-axis of a spectrogram (like Fig. 5 in the article) represents the frequency of each sine wave, the y-axis the magnitude (amplitude or more aptly the 'power') of each sine wave in the frequency spectrum.