Why use PSD to analyze a signal instead of its Fourier Transform?
The power spectral density (PSD) is a natural measure of the signal's power content with respect to frequency. A central part of non-parametric signal processing is to provide a &quot;best&quot; estimate  of the &quot;true&quot; PSD from knowing only one or some &quot;realizations&quot; with finite length. By taking into account the influence of stationary random processes, it should be noted that the Fourier transform is not defined for processes with infinite energy.
However, by looking at the second-order properties (autocorrelation), the true PSD can be well-defined, and the Fourier transform of  the realization  (on a finite horizon) can be used to provide an estimate of it.