What are the applications of Fourier Transform Power Spectrum?

What are the main applications of Fourier Transform Power Spectrum? Can somebody clarify with some examples.

Also, what are the advantages of using Fourier Transform Power Spectrum over Fourier Transform?

What is the advantage of Fourier Transform Power Spectrum in case of Image Processing?

Thank you so much.

• Power spectrum is for random signals while Fourier transform more suitable is for deterministic. For example if you have a random modulated signal (like QPSK) you can compute the power spectrum using the Fourier transform of the autocorrelation function but you wouldn't be able to compute the Fourier transform directly. – Harris Sep 29 '15 at 22:49
• @Harris Can you please expound on the "if you have a random modulated signal (like QPSK) you can compute the power spectrum using the Fourier transform of the autocorrelation function" .Is it possible to provide some relevant references? – Giwrgos Rizeakos Sep 30 '15 at 15:10
• There is a fairly detailed section on Digital Communications by J. G. Proakis, on page 131. – Harris Sep 30 '15 at 18:12
• Can someone explain the advantage of power spectrum of in case of image analysis as compared to Fourier Transform? – Psi Lambda Delta Oct 5 '15 at 20:57