I have the following signal for which amplitude and phase spectrums have to be computed:
This exercise also has a solution which begins by deriving the signal twice.
Next, they say the spectral density function for the given signal is:
In my attempt to figure out how did they get to that, I found the derivative property of the Fourier transform in the few pages of notes I have(there should be an F above the equivalency sign):
$$x''(t) \Leftrightarrow (j\omega)^2X(j\omega) $$
It looks quite a lot to what they have, but I do not know what do from here in order to reach their equation(formula). Also, can this property be applied to this signal or it only applies to non-periodic signals?