How to transform data to a frequency spectrum?
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.