psd fft
Forier Transform (FT) carries both amplitude and phase information, and you can reconstruct entirely a signal from its FT.
PSD of a signal says about how the power (or energy) is distributed in frequency. You can not reconstruct a signal from it, because it does not have phase information.
PSD of a stochastic process (SP) is a characteristic of the ensemble of its realizations. Is can say, for example, what can you expect about the output power or distortion when you apply the signal (seen as a realization of the SP) to a filter.
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Z