I always encounter random noise frequency domain representation as PSD(not FFT), something like in the below plot:
Without diving into math too much, practically speaking can we always use FFT instead of PSD to characterize a random signal? If so, what is the reason to use on to the other method in practice?
It even gets a bit more complicated because most of the time the signal can have both random and periodic components. Imagine I measure the constant pressure flow with a transducer's analog output. But those signal I sample will have both periodic and aperiodic components and random noise etc. In such case, if we have sampled the signal with enough sampling rate, what method between FFT and PSD would be preferred?
I before studied some Fourier series and transform and used many times FFT functions on MATLAB or Python for freq. domain view of a signal. Why would one need PSD if FFT is enough to for all types of signals?
(Digital scopes, for instance, show real-time FFT of a signal but not PSD. So not always PSD and not always FFT is used. How to decide which one to go for?)