Fourier Transforms

In the following visualization, a time series (bottom left, black) is reconstructed (red), by a sum of many sinusoids (top left). On the right, the phase (top) and amplitude (bottom) of each sine wave is plotted.

Aperiodic Signal

In the following, the time series is an aperiodic, pink noise signal, decomposed by an FFT:

Note that in the above, the signal is completely non-rhythmic.

Despite the signal not being rhythmic, it can still be decomposed by a sum on sinusoids.

Periodic Signal

In the next signal, there is both an aperiodic component (pink noise), as well as a periodic component (a 10 Hz rhythm).

In the above signal, note how the prominent rhythm is fit by a sine wave which stands out from the other frequencies, capturing the higher power in this frequency.