A Guide on Spectral Methods Applied to Discrete Data in One Dimension

Figure 6

Two spectra of function (25). The difference between the natural spectrum in (a) and the normal discrete Fourier transform in (b) is the symmetry. In (a), there is a symmetric spectrum around zero, whereas in (b) the point of symmetry is . The dots in panel (a) indicate the result of the DFT of the modulated sampling series of (25). Note the exceptional first bin in (b), where the mean value is stored.

(a) Natural spectrum (arrows) and DFT spectrum (circles)

(b) Discrete spectrum